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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 Tate cohomology group ： ウィキペディア英語版 Tate cohomology group In mathematics, Tate cohomology groups are a slightly modified form of the usual cohomology groups of a finite group that combine homology and cohomology groups into one sequence. They were introduced by , and are used in class field theory. ==Definition== If ''G'' is a finite group and ''A'' a ''G''-module, then there is a natural map ''N'' from ''H''0(''G'',''A'') to ''H''0(''G'',''A'') taking a representative ''a'' to Σ ''g''(''a'') (the sum over all ''G''-conjugates of ''a''). The Tate cohomology groups $\backslash hat\; H^n(G,A)$ are defined by *$\backslash hat\; H^n(G,A)\; =\; H^n(G,A)$ for ''n''≥ 1. *$\backslash hat\; H^0(G,A)=$ quotient of ''H''0(''G'',''A'') by norms *$\backslash hat\; H^(G,A)=$ quotient of norm 0 elements of ''H''0(''G'',''A'') by principal norm 0 elements *$\backslash hat\; H^n(G,A)\; =\; H\_(G,A)$ for ''n''≤ −2. 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「Tate cohomology group」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.