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Sheaves of abelian groups
Sheaves of modules
6 other sections not shown
a-closed a-finitely a-progenerator a-torsion A°pp abelian groups assertions are equivalent assume Azumaya algebra Bcl(X bijection Br(X Brauer group closed subset coherent sheaf cohomology cokernel commutative ring Corollary defined denote divisorial End(E exact sequence finishes the proof finite type finitely presented following assertions foregoing functor in R-mod Gabriel filter hence Hom(E i e l idempotent kernel functor induces injective invertible sheaves Krull domain Krull scheme ln particular lndeed locally free locally noetherian locally of finite locally ringed space lt follows modules morphism f O_x-modules open affine open covering open neighborhood open subset Open(X p e K(a Pic(R Pic(S Pic(X Pic(Y Picard group positive integer presheaf prime ideal Proposition Let proves the assertion quasicoherent sheaf QY(E R-lattice R-module resp result sheaf of abelian sheaf of Qx-modules sheaf space sheaves Spec(R subcategory surjective topology torsionfree verify Y-Azumaya algebra Y-closed Y-invertible yields