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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 Equivariant K-theory ： ウィキペディア英語版 Equivariant K-theory :''For the topological equivariant K-theory, see topological K-theory.'' In mathematics, the equivariant algebraic K-theory is an algebraic K-theory associated to the category $\backslash operatorname^G(X)$ of equivariant coherent sheaves on an algebraic scheme ''X'' with action of a linear algebraic group ''G'', via Quillen's Q-construction; thus, by definition, :$K\_i^G(X)\; =\; \backslash pi\_i(B^+\; \backslash operatorname^G(X)).$ In particular, $K\_0^G(C)$ is the Grothendieck group of $\backslash operatorname^G(X)$. The theory was developed by R. W. Thomason in 1980s.〔Charles A. Weibel, (Robert W. Thomason (1952–1995) ).〕 Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. Equivalently, $K\_i^G(X)$ may be defined as the $K\_i$ of the category of coherent sheaves on the quotient stack $()$. (Hence, the equivariant K-theory is a specific case of the K-theory of a stack.) A version of the Lefschetz fixed point theorem holds in the setting of equivariant (algebraic) K-theory. == Fundamental theorems == Let ''X'' be an equivariant algebraic scheme. 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「Equivariant K-theory」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.