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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 Bloch's formula ： ウィキペディア英語版 Bloch's formula In algebraic K-theory, a branch of mathematics, Bloch's formula, introduced by Spencer Bloch for $K\_2$, states that the Chow group of a smooth variety ''X'' over a field is isomorphic to the cohomology of ''X'' with coefficients in the K-theory of the structure sheaf $\backslash mathcal\_X$; that is, ::$\backslash operatorname^q(X)\; =\; \backslash operatorname^q(X,\; K\_q(\backslash mathcal\_X))$ where the right-hand side is the sheaf cohomology; $K\_q(\backslash mathcal\_X)$ is the sheaf associated to the presheaf $U\; \backslash mapsto\; K\_q(U)$, ''U'' Zariski open subsets of ''X''. The general case is due to Quillen.〔For a sketch of the proof, besides the original paper, see http://www-bcf.usc.edu/~ericmf/lectures/zurich/zlec5.pdf〕 For ''q'' = 1, one recovers $\backslash operatorname(X)\; =\; H^1(X,\; \backslash mathcal\_X^$ *). (see also Picard group.) The formula for the mixed characteristic is still open. == References == *Daniel Quillen: Higher algebraic K-theory: I. In: H. Bass (ed.): Higher K-Theories. Lecture Notes in Mathematics, vol. 341. Springer-Verlag, Berlin 1973. ISBN 3-540-06434-6 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「Bloch's formula」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.