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Localization of Rings and Modules
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a-closed a-dim a-dimension a-domdim a-finitely a-torsion a-torsionfree affine algebra apply assertions are equivalent associated assume belongs canonical isomorphism closed subset Cohen-Macaulay coherent sheaf cohomology Coker commutative Corollary Let Cousin complex defined denote derived functors devissage dimension dualizing easily checks easily verifies exact sequence finishes the proof finite type finitely generated module finitely presented flabby foregoing Gorenstein Gorenstein ring graded hence HomR HomR(M htM(p idempotent kernel functor injective hull injective module injective resolution isomorphism Krull left exact Lemma local cohomology locally ringed spaces Math maximal ideal Moreover morphism noetherian ring Nonlinear Note obvious open subset p e K(a P(Aff positive integer presheaf prime ideals Proj Proof Let Proposition Let proves the assertion Qa(M Qa(R quasicoherent sheaf R-mod R-module resp result ringed space sheaves Spec stable submodule Supp Suppa(M surjective Sz(X topology torsion theory yields