Introduction to Grothendieck Duality Theory |
Contents
Preface | 5 |
Completions Primary Decomposition and Length | 15 |
2 | 24 |
Copyright | |
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algebraic artinian ring assertion follows assertion results assume canonical map closed point closed subscheme Cohen-Macaulay commutative diagram conditions are equivalent Corollary da/k defined Definition denoted depth dimension divisor étale morphism exact sequence exists faithfully flat field filtration finite A-module finite length finite type flat resp following conditions functor g is étale gl.hd hence holds homomorphism implies induction injective integer irreducible isomorphism k-algebra Let f locally free locally noetherian scheme locally of finite M-regular M/IM M/XM maximal ideal module morphism locally Nakayama's lemma noetherian local ring noetherian ring open immersion Ox-Module polynomial proj.dim Proof Proposition q an ideal quotient radicial regular local ring residue ringed space S-scheme schemes and f schemes locally smooth smooth morphisms Spec spectral sequence submodule subset Supp F Suppose surjective Theorem Tor₁ unramified morphisms whence