id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
800,670 | AMR-134-0042 | Selection Principles Milestone Problems — Problem 43 ([SakaiRez, Question 3.5], [reznicb]) | In [coc7] it is shown that
$C_p(X)$ has countable fan tightness as well as Reznichenko's property if, and only if,
each finite power of $X$ has the Hurewicz covering property.
Recently, Sakai found an exact dual of the Reznichenko property:
An open $\omega$-cover $\mathcal{U}$ of $X$ is
*$\omega$-shrinkable* if for eac... | Source list: Tsaban - Selection Principles in Mathematics: A Milestone of Open Problems (2003)
Source item: Problem 43
Source URL: https://arxiv.org/abs/math/0312182
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [SakaiRez, Question 3.5], [reznicb] | 3 | open | Tsaban | 2,003 | 10 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,671 | AMR-134-0043 | Selection Principles Milestone Problems — Problem 44 ([SakaiRez, Question 3.6]) | Another simply stated problem is the following.
Does $C_p(\mathbb{N})$ have the Reznicenko property? | Source list: Tsaban - Selection Principles in Mathematics: A Milestone of Open Problems (2003)
Source item: Problem 44
Source URL: https://arxiv.org/abs/math/0312182
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [SakaiRez, Question 3.6] | 3 | open | Tsaban | 2,003 | 10 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,672 | AMR-134-0044 | Selection Principles Milestone Problems — Problem 45 ([SakaiRez, Question 2.8]) | A family $\mathcal{P}$ of subsets of of a space $Y$ is a *$\pi$-network*
at $y\in Y$ if every neighborhood of $y$ contains some element of
$\mathcal{P}$.
$Y$ is a *Pytkeev space* if for each $y\in Y$ and
$A\subseteq Y$ such that $y\in\overline{A}\setminus A$,
there exists a countable $\pi$-network at $y$
which consists... | Source list: Tsaban - Selection Principles in Mathematics: A Milestone of Open Problems (2003)
Source item: Problem 45
Source URL: https://arxiv.org/abs/math/0312182
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [SakaiRez, Question 2.8] | 3 | open | Tsaban | 2,003 | 10 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,673 | AMR-134-0045 | Selection Principles Milestone Problems — Problem 46 ([SakaiRez, Question 2.9]) | If all finite powers of $X$ satisfy $\mathsf{U}_{\mathrm{fin}}(\Gamma,\Gamma)$,
then every open $\omega$-cover of $X$ is $\omega$-shrinkable [SakaiRez],
thus a positive solution to the following problem would suffice.
Assume that $C_p(X)$ is a Pytkeev space. Is it true that all finite powers of
$X$ satisfy $\mathsf{U}... | Source list: Tsaban - Selection Principles in Mathematics: A Milestone of Open Problems (2003)
Source item: Problem 46
Source URL: https://arxiv.org/abs/math/0312182
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: [SakaiRez, Question 2.9] | 3 | open | Tsaban | 2,003 | 10 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,674 | AMR-135-0001 | Holomorphic Foliation Theory — Problem 1 | Instead of considering the weighted current $\tau^a_r$, we can consider an un-weighted current (*Ahlfors current*)
$$\sigma_r^a:={1\over A(r)} (\phi_a)_*[\mathbb{D}(r)] \qquad \text{with} \qquad A(r):=\int_{\mathbb{D}(r)} \phi_a^*(\omega).$$
Do we have $\sigma_r^a\to T$ as $r$ tends to $1$ for $T$-almost every $a$ ? | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,675 | AMR-135-0002 | Holomorphic Foliation Theory — Problem 2 | Assume that $\mathscr{F}$ is a foliation of degree $d\geq 2$ with non-hyperbolic singularities. Describe the
${dd^c}$-closed positive currents, directed by the foliation. In which case diffuse positive closed
currents directed by the foliation do exist ? | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,676 | AMR-135-0003 | Holomorphic Foliation Theory — Problem 3 | Let $\mathscr{H}_d$ denote the set of foliations of degree $d$ with only hyperbolic singularities. This is an open real Zariski dense set in $\mathscr{B}_d$. It is easy to show that $\mathscr{B}_d^{a}\cap\mathscr{H}_d$ is an analytic set [FS3] because one can bound the degree of the curve, when all singularities are hy... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 3
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,677 | AMR-135-0004 | Holomorphic Foliation Theory — Problem 4 (Anosov) | Consider foliations on $\mathbb{P}^2$. Recall that $\mathscr{B}_d$ denote the space of holomorphic foliations of geometric degree $d$ on $\mathbb{P}^2$. Let $\mathscr{A}_d$ denote the space of foliations given in an affine coordinate chart $\mathbb{C}^2$ in $\mathbb{P}^2$ by a vector field
$$Z:=P(z,w) {\partial \over \... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 4
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Anosov | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,678 | AMR-135-0005 | Holomorphic Foliation Theory — Problem 5 | Let $\mathscr{F}$ be a holomorphic foliation on $\mathbb{P}^2$. Denote by $\mathrm{sing}(\mathscr{F})$ the singular set of $\mathscr{F}$ which is finite.
Is it true that for every leaf $L$ of $\mathscr{F}$, we have $\overline L\cap \mathrm{Sing}(\mathscr{F})\not=\varnothing$ ? | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,679 | AMR-135-0006 | Holomorphic Foliation Theory — Problem 6 | The question is quite old and is due to Camacho-Lins Neto-Sad [CLS]. The problem is also discussed in [FS3]. The answer is positive if $\mathscr{F}$ admits a directed positive closed $(1,1)$-current $T$, in particular, when $\mathscr{F}$ has an invariant algebraic curve. The support of this current $T$ should contain a... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 6
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,680 | AMR-135-0007 | Holomorphic Foliation Theory — Problem 7 | (i) Assume that $\mathscr{F}$ is a foliation of geometric degree $d\geq 2$ on $\mathbb{P}^2$ with the line at infinity invariant and having only hyperbolic singularities. Do the leaves, except for the compact curves, have Green functions ?
(ii) More generally, assume that $\mathscr{F}$ is in $\mathscr{B}_d$ with $d\ge... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,681 | AMR-135-0008 | Holomorphic Foliation Theory — Problem 8 | Construct holomorphic minimal foliation (resp. lamination) on a compact complex manifold with uncountably many extremal ${dd^c}$-closed, non-closed, currents
directed by the foliation (resp. lamination). | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,682 | AMR-135-0009 | Holomorphic Foliation Theory — Problem 9 | Let $Z$ be a holomorphic vector field in $\mathbb{C}^2$.
(i) Is it possible to have a set of positive measure of leaves covered by $\mathbb{C}$ and another set of positive measure of leaves covered by the unit disc ?
(ii) If a non-pluripolar set of leaves are parabolic, are all leaves parabolic ?
(iii) Find conditio... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 9
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,683 | AMR-135-0010 | Holomorphic Foliation Theory — Problem 10 | Let $Z$ be a holomorphic vector field in $\mathbb{C}^k$ which is not the product of a polynomial vector field with a holomorphic function.
Let $\phi$ be the uniformization of a leaf $L$. The source could be $\mathbb{C}$ or the unit disc. Consider the Nevanlinna currents
$$\tau^\phi_r:={1\over T(r)} \phi_*\Big(\log^+{r\... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 10
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,684 | AMR-135-0011 | Holomorphic Foliation Theory — Problem 11 | Find the minimal growth of the Nevanlinna characteristic function $T_h$ for $h\in\mathscr{U}$, where
$$T_h(r):=\int_0^r {dt \over t} \int_{\mathbb{D}(t)} h^*(\omega)$$
and $\omega$ is the Fubini-Study form on $\mathbb{P}^1$. | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 11
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,685 | AMR-135-0012 | Holomorphic Foliation Theory — Problem 12 | Recently, Benjamin Weiss has proved the existence of non-trivial probability measures on $\mathscr{H}$ which are invariant by the above translation operator, see [Weiss]. These measures are studied in particular by Buhovsky, Gl\"ucksam, Logunov and Sodin [BGLS]. A measure is *non-trivial* if it gives zero measure to th... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 12
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,686 | AMR-135-0013 | Holomorphic Foliation Theory — Problem 13 | Consider a complex manifold $M$ of dimension $n$ which is homogeneous under the action of a Lie group $G$. Let $\mathscr{M}$ denote the space of holomorphic maps from $M$ to $\mathbb{P}^n$, endowed with the topology of uniform convergence on compact sets. The group $G$ acts on this space.
(i) Under which conditions th... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 13
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,687 | AMR-135-0014 | Holomorphic Foliation Theory — Problem 14 | Explore the above properties for the following classes of maps in $\mathbb{C}^n$ : biholomorphisms of $\mathbb{C}^n$ and volume preserving (resp. symplectic) automorphisms of $\mathbb{C}^n$ (resp. $\mathbb{C}^n$ with $n$ even). | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 14
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,688 | AMR-135-0015 | Holomorphic Foliation Theory — Problem 15 | In order to study foliations with leaves of dimension larger than $1$, what is the right notion which substitutes directed ${dd^c}$-closed currents in dimension $1$ that should be considered ?
Such objects should permit to develop the ergodic theory for these foliations. | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 15
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,689 | AMR-135-0016 | Holomorphic Foliation Theory — Problem 16 | Construct non-elementary foliations $\mathscr{F}$ in $\mathbb{P}^k$ with leaves of dimension larger than $1$ and such that every leaf does not contain a compact curve. | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 16
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,690 | AMR-135-0017 | Holomorphic Foliation Theory — Problem 17 | Is it always possible to approximate the foliation $\mathscr{F}$ by foliations in $\mathbb{C}^k$ or\break $\mathbb{P}^k$ ? More precisely, is it always possible to approximate the forms $\alpha_j$, uniformly on compact sets of $\mathbb{D}^k$, by entire forms (resp. polynomial forms) $\alpha_{j,n}$ which still satisfy t... | Source list: Dinh, Sibony - Some Open Problems on Holomorphic Foliation Theory (2018)
Source item: Problem 17
Source URL: https://arxiv.org/abs/1807.05640
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dinh, Sibony | 2,018 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,691 | AMR-136-0001 | Open Problems on Central Simple Algebras — Problem 1 | Perhaps the most important open problem in the theory of central simple algebras is:
Given a prime $p$, construct a non-cyclic division algebra of degree $p$ over some field $F$. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,692 | AMR-136-0002 | Open Problems on Central Simple Algebras — Problem 2 | As mentioned above, the smallest non-crossed product $p$-algebras known have degree $p^3$. Therefore even the following is open:
Determine whether $p$-algebras of degree $p^2$ are crossed products. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,693 | AMR-136-0003 | Open Problems on Central Simple Algebras — Problem 3 | In view of the fact that all known examples of non-crossed product algebras occur over fields of cohomological dimension at least 3, it is natural to ask:
If $F$ has cohomological dimension at most 2, is every central simple $F$-algebra a crossed product? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 3
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,694 | AMR-136-0004 | Open Problems on Central Simple Algebras — Problem 4 | Determine the smallest splitting group(s) of an $F$-division algebra $A$ arising
from the Galois closure of a maximal subfield of $A$. Determine in particular whether
every $A$ of degree $n$ has a separable maximal subfield whose Galois closure has group the alternating group $A_n$. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 4
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,695 | AMR-136-0005 | Open Problems on Central Simple Algebras — Problem 5 | Determine whether every division algebra is split by an abelian group,
and find degree bounds over specific fields. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,696 | AMR-136-0006 | Open Problems on Central Simple Algebras — Problem 6 | Determine groups $G$ and $G'$ and conditions on $F$ under which $G\Rightarrow_F G'$.
In particular:
- Determine, for $m$ prime-to-$p$, whether $C_p\rtimes C_m\Rightarrow_F C_p\times C_m$.
- Determine whether all quasi-symbols are cyclic. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 6
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,697 | AMR-136-0007 | Open Problems on Central Simple Algebras — Problem 7 | {\textrm{[Albert:cyclics, p. 126]}}
Is the $n$-torsion subgroup $\operatorname{Br}_p[n](F)$ generated by the classes of cyclic algebras of degree (dividing) $n$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,698 | AMR-136-0008 | Open Problems on Central Simple Algebras — Problem 8 | - *$F$ contains a primitive $n$-th root of unity.* This was pointed out above.
The Merkurjev-Suslin theorem, which establishes an isomorphism between
$K^M_2(F) / nK^M_2(F)$ and ${\text\mathrm{H}}^2(F,\mu_n^{\otimes 2})$, is now
a special case of the recently-proved Bloch--Kato Conjecture.
The smallest open case for $n... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,699 | AMR-136-0009 | Open Problems on Central Simple Algebras — Problem 9 | (These problems are related to the following very
special question stated by M. Mahdavi-Hezavehi: \emph{If the
multiplicative group $F^\times$ is divisible, does it follow that
$\operatorname{Br}(F)$ is zero?} The answer is ``yes'' if $\operatorname{Br}(F)$ is generated by
cyclic algebras, because cyclic algebras are s... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 9
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,700 | AMR-136-0010 | Open Problems on Central Simple Algebras — Problem 10 | And one can ask the weaker question:
Is $\operatorname{Br}_p[n](F)$ generated by algebras of degree $n$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 10
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,701 | AMR-136-0011 | Open Problems on Central Simple Algebras — Problem 11 | Suppose $m$ and $n$
have the same prime factors, $m\mid n$,
and $\operatorname{Br}_p[m](F)$ is generated by cyclic algebras. Let $\ell_F(m,n)$
denote the minimal number such that every central simple $F$-algebra
of degree $n$ and period (dividing) $m$ is similar to a tensor
product of $\ell_F(m,n)$ cyclic algebras of d... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 11
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,702 | AMR-136-0012 | Open Problems on Central Simple Algebras — Problem 12 | If $F$ is finitely generated over a field $F_0$ with $\operatorname{Br.\!dim}(F_0)$ finite, is $\operatorname{Br.\!dim}(F)$ necessarily finite?
It is natural to start by considering only certain fields $F_0$. For example, suppose that $F$ has prime characteristic $p$ and we take $F_0$ to be its prime field, so $\opera... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 12
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,703 | AMR-136-0013 | Open Problems on Central Simple Algebras — Problem 13 | Define a notion of ``dimension'' for some class of fields $F$ such that
\[
\operatorname{Br.\!dim}(F) \le \dim F - 1 \quad \text{and} \quad \dim(F(t)) = \dim F + 1.
\]
One possibility would be to set a $C_i$ field to have dimension $i$. The notion of cohomological dimension is obviously not the right one in view of Mer... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 13
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,704 | AMR-136-0014 | Open Problems on Central Simple Algebras — Problem 14 | To simplify the discussion note the result of Katsylo [Katsylo] and Schofield [Schofield] that if $n = ab$ for $a$ and $b$ relatively prime, then $Z(F,n)$ is stably isomorphic to the field compositum $Z(F,a) Z(F,b)$. Similar statements are possible for the $Z_m(F,n)$ and $Z_H(F,n)$. This often (but not always) allows r... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 14
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,705 | AMR-136-0015 | Open Problems on Central Simple Algebras — Problem 15 | There are a few results for the $Z_m(F,n)$. The field $Z_2(F,4)$ is stably rational by Saltman [Salt:symp], and Saltman--Tignol [SaltTig] showed that $Z_2(F,8)$ is retract rational. Beneish [Beneish:28] showed that $Z_2(F,8)$ is stably rational.
Finally, we leave to the well-read reader to prove that when $H \subset S_... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 15
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,706 | AMR-136-0016 | Open Problems on Central Simple Algebras — Problem 16 | Compute the essential dimension and the essential $p$-dimension of
$\operatorname{PGL}_{n}$.
In particular:
- Compute $\mathrm{ed}_F(\operatorname{PGL}_4)$ when $\operatorname{char} F=2$.
- Compute $\mathrm{ed}_F(\operatorname{PGL}_5)$. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 16
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,707 | AMR-136-0017 | Open Problems on Central Simple Algebras — Problem 17 | Determine structural conclusions about central simple algebras
from essential ($p$-)dimension bounds.
- Calculate bounds for $\mathrm{ed}(\operatorname{CPAlg}_n)$ and $\mathrm{ed}(\mathrm{Alg}_G)$.
- Compute the difference $\mathrm{ed}(\mathrm{Alg}_G)-\mathrm{ed}(G)$.
- If $\mathrm{ed}(\operatorname{CPAlg}_n)=\mathr... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 17
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,708 | AMR-136-0018 | Open Problems on Central Simple Algebras — Problem 18 | Compute $\mathrm{ed}_F(\operatorname{GL}_{8}/\mu_{2})$ when $\operatorname{char} F = 2$; $\mathrm{ed}_F(\operatorname{GL}_{16}/\mu_{2})$ when $\operatorname{char} F \ne 2$; and $\mathrm{ed}_F(\operatorname{GL}_{p^2}/\mu_{p})$ for odd primes $p$ and all $F$. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 18
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,709 | AMR-136-0019 | Open Problems on Central Simple Algebras — Problem 19 | Suppose $\sigma$ is an anisotropic orthogonal or symplectic
involution on a central simple algebra $A$ over a field $F$. Does
$\sigma$ remain anisotropic after scalar extension to any odd-degree
field extension of $F$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 19
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,710 | AMR-136-0020 | Open Problems on Central Simple Algebras — Problem 20 | Suppose $\sigma$ is an anisotropic orthogonal involution on a
central simple algebra $A$ over a field $F$. Does $\sigma$ remain
anisotropic after scalar extension to the function field $F_A$ of the
Severi--Brauer variety of $A$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 20
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,711 | AMR-136-0021 | Open Problems on Central Simple Algebras — Problem 21 | Let $G$ be an absolutely almost simple linear algebraic group that is
anisotropic over $F$. Does $G$ remain anisotropic over every finite
extension $K/F$ of dimension not divisible by any prime in $S(G)$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 21
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,712 | AMR-136-0022 | Open Problems on Central Simple Algebras — Conjecture 24 (Tate's Conjecture T) | Let $\ell\neq p$ be a prime. Let $P_2(X,t)$ be the characteristic
polynomial of the action of the (geometric) Frobenius morphism on the
$\ell$-adic cohomology ${\text\mathrm{H}}^2(\overline{X},{\mathbb{Q}}_{\ell}(1))$, where $\overline{X} = X
\times_{k} k_{{\mathrm{sep}}}$. Let $\operatorname{NS}(X) = \mathrm{Pic}(X)/\... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Conjecture 24
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Tate's Conjecture T | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,713 | AMR-136-0023 | Open Problems on Central Simple Algebras — Conjecture 27 (BSD Conjecture) | Let $K$ be a global field of characteristic $p$, $A$ an abelian
$K$-variety, and $L^*(A,s)$ the $L$-function of $A$ with respect to a
suitably normalized Tamagawa measure. Then $L^*(A,s)$ has an analytic
continuation to the complex plane and
$$
\lim_{s\to 1} \frac{L^*(A,s)}{(s-1)^{r}} = \frac{|\mathrm{III}(A)|
|\det(h_... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Conjecture 27
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: BSD Conjecture | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,714 | AMR-136-0024 | Open Problems on Central Simple Algebras — Problem 28 | Given a geometrically connected, smooth, projective surface $X$ over a
finite field $k$, is there a non-degenerate alternating pairing on
$\operatorname{Br}(X)(2)$ with values in ${\mathbb{Q}}/{\mathbb{Z}}$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 28
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,715 | AMR-136-0025 | Open Problems on Central Simple Algebras — Problem 29 | Is there a structural criterion for the tensor product
$A\otimes_F B$ of two $F$-division algebras $A$ and $B$ to have a zero divisor? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 29
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,716 | AMR-136-0026 | Open Problems on Central Simple Algebras — Problem 30 | Suppose $(a,b)_n$ and $(c,d)_n$ are symbol algebras
of degree $n$ over $F$, and $(a,b)_n \otimes_F (c,d)_n$ has index $< n^2$.
Are there necessarily symbol algebras $(a',b')_n$ and $(c',d')_n$ that share a common maximal
subfield and such that $(a, b)_n \otimes_F (c, d)_n \cong (a',b')_n \otimes_F (c', d')_n$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 30
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,717 | AMR-136-0027 | Open Problems on Central Simple Algebras — Problem 31 | One can also consider splitting fields instead of maximal
subfields:
If $\operatorname{ind}(A\otimes_F B) < \operatorname{ind} (A) \operatorname{ind}(B)$,
what are the common splitting fields for the $F$-division algebras $A$ and $B$? | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 31
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,718 | AMR-136-0028 | Open Problems on Central Simple Algebras — Conjecture 32 (Amitsur's Conjecture) | He then posed the following converse of (2):
If $A$ and $B$ have the same degree and generate the same subgroup of
the Brauer group, then $F(A)$ and $F(B)$ are isomorphic. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Conjecture 32
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Amitsur's Conjecture | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,719 | AMR-136-0029 | Open Problems on Central Simple Algebras — Problem 33 | Determine whether two division algebras that have the same splitting fields in a given
class (say finite, or of transcendence degree at most one), necessarily generate the
same subgroup in the Brauer group. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 33
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,720 | AMR-136-0030 | Open Problems on Central Simple Algebras — Problem 34 | The smallest open case appears to be:
Determine whether two division algebras of degree $3$ that have the same splitting
fields of transcendence degree $\leq 1$ generate the same subgroup of the Brauer group. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 34
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,721 | AMR-136-0031 | Open Problems on Central Simple Algebras — Problem 35 | Show that if $F$ is a field which is finitely generated over a
prime field or over an algebraically closed field, then any two
quaternion division algebras having the same finite splitting fields (or even
just the same maximal subfields) must be isomorphic. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 35
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,722 | AMR-136-0032 | Open Problems on Central Simple Algebras — Problem 37 | Let $F$ be a field and $G$ a finite group.
We say $G$ is *$F$-admissible* if there exists a
$G$-crossed product $F$-division algebra $A$.
Determine which groups are $F$-admissible, for a field $F$. | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 37
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,723 | AMR-136-0033 | Open Problems on Central Simple Algebras — Problem 38 | This problem is an extension of
the inverse Galois problem, and is especially interesting for $F={\mathbb{Q}}$.
It appears as part of Problem 5 in [Am:surv].
The next problem, also known as the \emph{${\mathbb{Q}}$-admissibility conjecture},
was first recognized in [Schacher:th1].
Prove every Sylow-metacyclic group i... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 38
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,724 | AMR-136-0034 | Open Problems on Central Simple Algebras — Conjecture 39 | The ``if'' direction can be found in [Vos, p. 186]. The full theorem amounts to combining the results from ibid.\ with [Gille:KT, Th. 5.9]. Gille's theorem furthermore shows that the conditions are equivalent to the abstract group $\operatorname{SL}_r(A)(L)$ being ``projectively simple" for every extension $L/F$ and ev... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Conjecture 39
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,725 | AMR-136-0035 | Open Problems on Central Simple Algebras — Problem 40 | Amongst the first examples one sees, probably the fields ${\mathbb{R}}$ or iterated Laurent series ${\mathbb{R}}((x_1))((x_2))\cdots((x_n))$ are the only ones whose Brauer group is nonzero and finite. This leads to the following naive question:
For which natural numbers $n$ is there a field $F$ such that $|\!\operator... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Problem 40
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,726 | AMR-136-0036 | Open Problems on Central Simple Algebras — Conjecture 41 | [Brumer--Rosen \protect{[BrumerRosen]}]
For a given field $F$ and each prime $p$, one of the following holds:
\renewcommand{\alph{enumi}}{\alph{enumi}}
- $(\operatorname{Br} F)_p = 0$.
- $(\operatorname{Br} F)_p$ contains a nonzero divisible subgroup.
- $p = 2$ and $(\operatorname{Br} F)_2$ is an elementary abelian... | Source list: Auel, Brussel, Garibaldi, Vishne - Open Problems on Central Simple Algebras (2010)
Source item: Conjecture 41
Source URL: https://arxiv.org/abs/1006.3304
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Auel, Brussel, Garibaldi, Vishne | 2,010 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,727 | AMR-137-0001 | Open Problems in Topological Algebra — Problem 1 (Choban) | Is every topological group a quotient group of a
zero-dimensional topological group of the same weight? When an
almost metrizable topological group is a quotient of a
zero-dimensional group of the same weight? | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Choban | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,728 | AMR-137-0002 | Open Problems in Topological Algebra — Problem 2 (Choban) | Under which conditions is the free
universal algebra of an uncountable signature over a metrizable
space $X$ paracompact? In particular, is the free topological
linear space $L(X)$ of $X$ over the discrete field of real numbers
paracompact? | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Choban | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,729 | AMR-137-0003 | Open Problems in Topological Algebra — Problem 3 (Protasov) | For a topological space $X$ let $S(X)\subset X^X$ be the semigroup
of all continuous selfmappings of $X$ endowed with the topology of
pointwise convergence (i.e., the topology inherited from the
Tychonov product $X^X$). A topological space $X$ is called *homogeneous* if for any points $x_1,x_2\in X$ there is a
homemorp... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 3
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Protasov | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,730 | AMR-137-0004 | Open Problems in Topological Algebra — Problem 4 (Protasov) | The answer is positive provided $X$ has a base of the topology,
consisting of pairwise homeomorphic clopen subsets, see
[Pr1].
Is the semigroup $S(X)$ right bounded
for any zero-dimensional homogeneous space $X$? | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 4
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Protasov | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,731 | AMR-137-0005 | Open Problems in Topological Algebra — Problem 5 (Protasov) | Let $X$ be a topological space. A subgroup $H$ of $S(X)$ is called
*distal* if for any distinct points $x_1,x_2\in X$ and any
point $x\in X$ there is a neighborhood $U$ of $x$ such that
$\{h(x_1),h(x_2)\}\not\subset U$ for all $h\in H$. It is proven in
[Pr1, Theorem 4] that a left bounded subgroup $H\subset S(X)$
is di... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Protasov | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,732 | AMR-137-0006 | Open Problems in Topological Algebra — Problem 6 (Protasov) | It is well known that $\sigma$-compact topological groups have
countable cellularity [Tk] while compact topological groups
support a strictly positive probability measure (i.e., a Borel
probability measure $\mu$ such that $\mu(U)>0$ for any nonempty
open subset $U$ of the group). Recently T. Banakh and O. Ravsky
[BR] (... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 6
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Protasov | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,733 | AMR-137-0007 | Open Problems in Topological Algebra — Problem 7 (Protasov) | Does every zero-dimensional compact
homogeneous space admit the structure of a left topological group? (This problem was answered in negative by Banakh in [T.Banakh, *A homogeneous first-countable zero-dimensional compactum failing to be a left-topological group*, Mat. Stud.29 (2008) 215--217].)
In particular, does the... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Protasov | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,734 | AMR-137-0008 | Open Problems in Topological Algebra — Problem 8 (Protasov) | Can every non-discrete topological group $G$ be algebraically
generated by a nowhere dense subset? (The answer to Problem 6 is ``No'': under CH the topological group $\mathbb{R}^{\omega_1}$ contains a dense non-separable subgroup $G$ such that each meager subset of $G$ generates a metrizable separable subgroup of $G$; ... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Protasov | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,735 | AMR-137-0009 | Open Problems in Topological Algebra — Problem 9 (Guran) | A paratopological group $G$ is *left $\omega$-bounded* (resp.
*right $\omega$-bounded*) if for any neighborhood $U\subset G$
of the origin there is a countable subset $F\subset G$ with $G=FU$
(resp. $G=UF$); $G$ is *$\omega$-bounded* if it is both left
and right $\omega$-bounded.
Is a paratopological group $G$ left
$\... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 9
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Guran | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,736 | AMR-137-0010 | Open Problems in Topological Algebra — Problem 10 (Banakh) | Is there a (metrizable) $o$-bounded
topological group $G$ such that the player I has a winning
strategy in the game OF($G$)? | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 10
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Banakh | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,737 | AMR-137-0011 | Open Problems in Topological Algebra — Problem 11 (Banakh) | Such a group, if exists, cannot be analytic and abelian (more
generally, a SIN-group). We remind that a topological space $X$ is
analytic if it is a metrizable continuous image of a separable
complete metric space. On the other hand, the group ${\mathbb{Z}}^\omega$ contains a dense $o$-bounded $G_\delta$-subset $A$ suc... | Source list: Banakh, Choban - Some Open Problems in Topological Algebra (2012)
Source item: Problem 11
Source URL: https://arxiv.org/abs/1202.1619
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Banakh | 3 | open | Banakh, Choban | 2,012 | 7 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,738 | AMR-138-0001 | Banach Spaces and Ramsey Theory — Problem 1 | Recall that the *Banach-Mazur distance* between two isomorphic Banach spaces
$X$ and $Y$ (not necessarily infinite-dimensional) is defined by
\[ d_{BM}(X,Y)=\inf\big\{\|T\|\cdot\|T^{-1}\|: T:X\to Y \text{ is an isomorphism}\big\}.\]
For every $n\in\mathbb{N}$ define
\[ R^n_\infty=\max\big\{ d_{BM}(X,\ell^n_\infty): \ma... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 1
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,739 | AMR-138-0002 | Banach Spaces and Ramsey Theory — Problem 2 | \emph{(Elton unconditionality constant -- S. J. Dilworth, E. Odell, Th. Schlumprecht and A. Zs\'{a}k
[DOSZ])} Does there exist $M\geqslant 1$ such that $K(\delta)\leqslant M$ for every $0<\delta\leqslant
1$? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 2
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,740 | AMR-138-0003 | Banach Spaces and Ramsey Theory — Problem 3 | *(Rosenthal basis problem -- H. P. Rosenthal [FPR])*
Is it true that every Rosenthal basis $(x_n)$ is equivalent to the standard
unit vector basis of $c_0$ or $\ell_p$ for some $1\leqslant p<+\infty$? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 3
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,741 | AMR-138-0004 | Banach Spaces and Ramsey Theory — Problem 4 | *(Unique spreading model problem -- S. A. Argyros [AOST])*
Let $X$ be a reflexive Banach space such that $|\mathrm{SP_w}(X)/\sim|=1$ (i.e. all
normalized weakly null sequences in $X$ generate a unique spreading model
up to equivalence). Is it true that the unique spreading model is equivalent
to the standard unit vecto... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 4
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,742 | AMR-138-0005 | Banach Spaces and Ramsey Theory — Problem 5 | *(Countable spreading models problem -- S. J. Dilworth, E. Odell and B. Sari [DOS])*
Let $X$ be a reflexive Banach space such that $|\mathrm{SP_w}(X)/\sim|\leqslant \aleph_0$.
Does there exist a normalized weakly null sequence in $X$ generating a spreading model
equivalent to the standard unit vector basis of $c_0$ or ... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 5
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,743 | AMR-138-0006 | Banach Spaces and Ramsey Theory — Problem 6 | *(Block homogeneous basis problem -- see [FR])*
Let $X$ be a Banach space with a normalized block homogeneous Schauder
basis. Is it true that $X$ is isomorphic to $c_0$ or $\ell_p$ for some
$1\leqslant p<+\infty$? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 6
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,744 | AMR-138-0007 | Banach Spaces and Ramsey Theory — Problem 7 | Although it is known that every separable non-Hilbertian Banach space contains
two non-isomorphic subspaces, we point out that there are several
related open problems. The following one is probably the most natural.
*(G. Godefroy [Go])*
Let $X$ be a separable non-Hilbertian Banach space. Is it true that there
exists a... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 7
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,745 | AMR-138-0008 | Banach Spaces and Ramsey Theory — Problem 8 | Let $X$ be a separable Banach space which fails to have type $2-
$ (or fails
to have co-type $2+
$) for some $
>0$. Is it true that $X$ contains
continuum many pairwise non-isomorphic subspaces? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 8
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,746 | AMR-138-0009 | Banach Spaces and Ramsey Theory — Problem 9 | *(Complemented Subspace Problem for $C[0,1]$ -- see [BP-new,LW-new,Pe1])*
Is it true that every complemented subspace of $C[0,1]$ is isomorphic to a $C(K)$ space
for some closed subset $K$ of $[0,1]$. | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 9
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,747 | AMR-138-0010 | Banach Spaces and Ramsey Theory — Problem 10 | *(Fixing properties of operators on $C[0,1]$ -- H. P. Rosenthal [Ro2])*
Let $T:C[0,1]\to C[0,1]$ be a bounded linear operator and $X$ be a separable Banach
space not containing a copy $c_0$. Assume that the operator $T$ fixes a copy of $X$.
Is it true that $T$ fixes a copy of $C[0,1]$? Equivalently, is it true that the... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 10
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,748 | AMR-138-0011 | Banach Spaces and Ramsey Theory — Problem 11 | The *Distortion Problem* is discussed in detail in [OS-new].
A surprising phenomenon observed so far is that ``most" distortable
Banach spaces are arbitrarily distortable.
*(Bounded distortion -- see [OS-new])* Does there exist a boundedly distortable
Banach space? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 11
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,749 | AMR-138-0012 | Banach Spaces and Ramsey Theory — Problem 13 | *(Converse Aharoni problem -- see [BL,Kalton])*
Let $X$ be a separable Banach space with the property that every separable
Banach space is Lipschitz isomorphic to a subset of $X$. Is it
true that $X$ contains a copy of $c_0$? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 13
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,750 | AMR-138-0013 | Banach Spaces and Ramsey Theory — Problem 14 | Recall the very old result due to S. Banach and S. Mazur saying that every
infinite-dimensional Banach space has an infinite basic sequence. It turns out
that the dual version of this *Basic Sequence Problem* is still widely open.
\emph{(S. Banach [B] -- A. Pe{\l}czy\'{n}ski [Pe0])}
Does every infinite-dimensional Ban... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 14
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,751 | AMR-138-0014 | Banach Spaces and Ramsey Theory — Problem 15 | So the problem of S. Banach and A. Pe{\l}czy\'{n}ski now becomes the following.
*(Separable quotient problem)* Does every infinite-dimensional Banach
space have a non-trivial infinite-dimensional separable quotient? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 15
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,752 | AMR-138-0015 | Banach Spaces and Ramsey Theory — Problem 16 | Are the following equivalent assuming the P-ideal dichotomy?
(1) Every non-separable Banach space has an uncountable biorthogonal system.
(2) $\mathfrak{b}=\aleph_2$. | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 16
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,753 | AMR-138-0016 | Banach Spaces and Ramsey Theory — Problem 17 | Recall that a *support set* in a Banach space $X$ is a nonempty convex set
$C$ with the property that every point $x$ of $C$ is its support point, i.e. there
is a functional $f$ of $X$ such that
\[ f(x)=\inf\{f(y): y\in C\}<\sup\{f(y): y\in C\}. \]
The existence of a support set in every non-separable Banach space is a... | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 17
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,754 | AMR-138-0017 | Banach Spaces and Ramsey Theory — Problem 18 | This leaves however open the following interesting variant of Rolewicz's problem.
*(S. Todorcevic [To1])* Does every Banach space of density $>\aleph_1$
have a support set? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 18
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,755 | AMR-138-0018 | Banach Spaces and Ramsey Theory — Problem 19 | *(Unconditional basic sequences in non-separable spaces)*
Does every Banach space $X$ of density $>\mathfrak{c}$ have an infinite unconditional basic sequence? Does additional properties,
like reflexivity, make a difference? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 19
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,756 | AMR-138-0019 | Banach Spaces and Ramsey Theory — Problem 20 | On the other hand no consistent bounds, like the one of [DLT]
mentioned above, is known in this context. So the following problem is wide open.
Does every (respectively, every reflexive) Banach space of density $>\mathfrak{c}$
(respectively, of density $>\aleph_1$) has an infinite sub-symmetric basic
sequence? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 20
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,757 | AMR-138-0020 | Banach Spaces and Ramsey Theory — Problem 22 | *(D. H. Fremlin [Fr2])*
Is there a compact hereditary family of finite subsets of $\omega_1$ containing
the singletons and having the property that every finite subset of $\omega_1$
has a subset half of its size belonging to the family $\mathcal{F}$? | Source list: Dodos, Lopez-Abad - Banach Spaces and Ramsey Theory: Some Open Problems (2010)
Source item: Problem 22
Source URL: https://arxiv.org/abs/1006.2668
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Dodos, Lopez-Abad | 2,010 | 8 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,758 | AMR-139-0001 | Open Problems in the Theory of Ample Fields — Question 1 | Our first question can be simply stated as follows.
Is $\mathbb{Q}_\mathrm{ab}$ ample? | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Question 1
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,759 | AMR-139-0002 | Open Problems in the Theory of Ample Fields — Conjecture 2 (Shafarevich) | The importance of this question lies in the fact that, via Pop's results on ample fields,
a positive answer would give a proof of the following conjecture of Shafarevich, cf. [DD]:
The absolute Galois group $G_{\mathbb{Q}_\mathrm{ab}}$ of $\mathbb{Q}_\mathrm{ab}$ is a free profinite group. | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Conjecture 2
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Shafarevich | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,760 | AMR-139-0003 | Open Problems in the Theory of Ample Fields — Question 3 | Colliot-Th\'el\`ene observed that a field $K$ is ample whenever $G_K$ is a pro-$p$ group for some
prime number $p$, [ColliotThelene,JardenAmple].
This covers again in particular
the archimedean local fields $\mathbb{R}$ and $\mathbb{C}$.
Since pro-$p$ groups are prosolvable, and all local fields have prosolvable absolu... | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Question 3
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,761 | AMR-139-0004 | Open Problems in the Theory of Ample Fields — Question 4 | Another Galois theoretic property that the local fields ${\mathbb{Q}}_p$, $\mathbb{R}$, and $\mathbb{C}$
share, apart from having a prosovable absolute Galois group,
is that their absolute Galois groups are all finitely generated (as topological groups).
The following question occurs as a conjecture in [JunkerKoenigsma... | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Question 4
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,762 | AMR-139-0005 | Open Problems in the Theory of Ample Fields — Question 5 | Trivially, every ample field is virtually ample, and every virtually ample field is weakly ample.
One could think that every virtually ample field should be ample,
but no proof is known.
As evidence one usually refers to the fact that similar descent properties hold for
Henselian valued fields.
We want to ask more gene... | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Question 5
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,763 | AMR-139-0006 | Open Problems in the Theory of Ample Fields — Question 6 | A field $K$ is called **radically closed** if the multiplicative group $K^\times$ is divisible.
Any radically closed field contains all roots of unity and hence, by Kummer theory, has no solvable finite Galois extensions.
One would like to know the following:
Is every radically closed field ample? | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Question 6
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,764 | AMR-139-0007 | Open Problems in the Theory of Ample Fields — Conjecture 7 (Podewski) | An infinite field $K$ is called **minimal** if every subset $A\subseteq K$ which is definable
by a first-order formula in the language of rings is finite or cofinite.
For example, algebraically closed fields have this property,
and an old conjecture of Podewski says that they should be the only ones:
Every minimal fie... | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Conjecture 7
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: Podewski | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,765 | AMR-139-0008 | Open Problems in the Theory of Ample Fields — Conjecture 8 (D\`ebes-Deschamps) | D\`ebes and Deschamps combined these two conjectures into one.
A **regular solution** to an embedding problem $G\rightarrow\mathrm{Gal}(L/K)$ over $K$
is a solution $\gamma:\mathrm{Gal}(F/K(t))\rightarrow G$ to the induced embedding problem
$G\rightarrow\mathrm{Gal}(L/K)\cong\mathrm{Gal}(L(t)/K(t))$
over $K(t)$ such th... | Source list: Bary-Soroker, Fehm - Open Problems in the Theory of Ample Fields (2011)
Source item: Conjecture 8
Source URL: https://arxiv.org/abs/1106.1310
Accessed: 2026-10-16
Extraction: arxiv_latex
Notes and literature:
Attribution/Context: D\`ebes-Deschamps | 3 | open | Bary-Soroker, Fehm | 2,011 | 4 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,766 | AMR-140-0001 | Positively Curved Projective Varieties — Problem 1 | MRC fibrations are almost holomorphic by definition,
but they are not necessarily represented by holomorphic maps.
In fact, there is a projective variety $Z$ with Picard number one,
such that $Z$ is uniruled but not rationally connected,
which was constructed by Fujita (see [EIM20, Example 6.5] for details).
The variet... | Source list: Matsumura - Open Problems on Structure of Positively Curved Projective Varieties (2022)
Source item: Problem 1
Source URL: https://arxiv.org/abs/2211.09153
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Matsumura | 2,022 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,767 | AMR-140-0002 | Positively Curved Projective Varieties — Conjecture 2 | The following conjecture posed by Yau can be regarded as
an analogy of Mok's result for holomorphic sectional curvature.
[Yau's conjecture, {[Yau82, Problem 47]}]
If a compact K\"ahler manifold $X$ has positive holomorphic sectional curvature,
then $X$ is projective and rationally connected. | Source list: Matsumura - Open Problems on Structure of Positively Curved Projective Varieties (2022)
Source item: Conjecture 2
Source URL: https://arxiv.org/abs/2211.09153
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Matsumura | 2,022 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,768 | AMR-140-0003 | Positively Curved Projective Varieties — Problem 3 | [{[Mat18b, Problem 5.1]}]
Let $(X, g)$ be a compact K\"ahler manifold
with semi-positive holomorphic sectional curvature.
Assume that $n_{{\rm{tf}}}{(X, g)} = \dim X$.
$\bullet$ Does it hold that $h^{0}(X, \Omega_X^q)=0$ for any $q>0$?
$\bullet$ Is $X$ automatically projective? | Source list: Matsumura - Open Problems on Structure of Positively Curved Projective Varieties (2022)
Source item: Problem 3
Source URL: https://arxiv.org/abs/2211.09153
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Matsumura | 2,022 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
800,769 | AMR-140-0004 | Positively Curved Projective Varieties — Problem 4 | [cf. {[Mat18b, Problem 5.2]}]
Let $(X, g)$ be a compact K\"ahler manifold
with semi-positive holomorphic sectional curvature.
$\bullet$ Is the fundamental group of $X$ is an extension of a finite group
by $\mathbb{Z}^{\oplus 2m}$?
For an appropriate finite \'etale cover $X^* \to X$,
we consider its Albanese map $\al... | Source list: Matsumura - Open Problems on Structure of Positively Curved Projective Varieties (2022)
Source item: Problem 4
Source URL: https://arxiv.org/abs/2211.09153
Accessed: 2026-10-16
Extraction: arxiv_latex | 3 | open | Matsumura | 2,022 | 5 | 13 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 13,
"name": "amr_open_problem_lists",
"display_name": "AMR Open Problem Lists",
"description": "Open and partially solved problems collected from public source lists indexed by AMR, with per-record provenance and status notes.",
"slug": "amr-open-problem-lists",
"order_index": 13,
"created_at": "2... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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