Finite presentation of invertible sheaves #
An invertible sheaf is locally free on a one-element basis, so it is locally finitely presented. This file makes that implication available to the scheme-level sheaf API.
The general finite-presentation theorem for locally free data is in
TauCeti/Algebra/Category/ModuleCat/Sheaf/FinitePresentation.lean. The only additional step for
an invertible sheaf is finiteness of the local bases, supplied by their Subsingleton instances.
The main result is the instance
TauCeti.SheafOfModules.IsInvertible.isFinitePresentation. It applies over an arbitrary site;
the scheme-level finitely-presented-sheaf packaging is in
TauCeti/AlgebraicGeometry/FinitelyPresentedSheaf/Basic.lean.
This advances TauCetiRoadmap/JacobianChallenge/README.md, from Layer A's invertible sheaves to
Layer B's coherent sheaves. No formalization is vendored.
An invertible sheaf of modules is finitely presented.
The rank-one local bases give finite generating families, and the locally free presentations have no relations.