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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Grothendieck local duality ： ウィキペディア英語版 Grothendieck local duality In commutative algebra, Grothendieck local duality is a duality theorem for cohomology of modules over local rings, analogous to Serre duality of coherent sheaves. ==Statement== Suppose that ''R'' is a Cohen–Macaulay local ring of dimension ''d'' with maximal ideal ''m'' and residue field ''k'' = ''R''/''m''. Let ''E''(''k'') be a Matlis module, an injective hull of ''k'', and let be the completion of its dualizing module. Then for any ''R''-module ''M'' there is an isomorphism of modules over the completion of ''R'': : $\backslash operatorname\_R^i(M,\backslash overline\backslash Omega)\; \backslash cong\; \backslash operatorname\_R(H\_m^(M),E(k))$ where ''H''''m'' is a local cohomology group. There is a generalization to Noetherian local rings that are not Cohen–Macaulay, that replaces the dualizing module with a dualizing complex. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Grothendieck local duality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.