| import OAI.NumberTheory.PiExponent.Jets.AffineJetPolynomial | |
| namespace OAI | |
| noncomputable section | |
| namespace PiExponent.AffineJetCoefficientInterface | |
| open AlgebraicGeometry CategoryTheory | |
| open PiExponentSeshadri.Geometry | |
| open PiExponent.ExceptionalAffineChart | |
| variable {X : Scheme} {R : Type} [CommRing R] | |
| variable (j : Spec (CommRingCat.of R) ⟶ X) [IsOpenImmersion j] | |
| variable (A : LineBundle X) | |
| def Frame : Type := A.sheaf.restrict (chartOpen j).1.ι ≅ structureSheaf (chartOpen j).1.toScheme | |
| def Sections (n : ℕ) : Type := GlobalSections X (modulePow X A.sheaf n) | |
| def coefficient (n : ℕ) (e : Frame j A) : Sections A n → R := | |
| AffineJetPolynomial.polynomialCoefficient j A n e | |
| theorem coefficient_eq (n : ℕ) (e : Frame j A) (s : Sections A n) : | |
| coefficient j A n e s = AffineJetPolynomial.polynomialCoefficient j A n e s := rfl | |
| end PiExponent.AffineJetCoefficientInterface | |
| end | |
| end OAI | |