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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 Hodge–de Rham spectral sequence ： ウィキペディア英語版 Hodge–de Rham spectral sequence In mathematics, the Hodge–de Rham spectral sequence, also known as the Frölicher spectral sequence computes the cohomology of a complex manifold. ==Description of the spectral sequence== The spectral sequence is as follows: :$H^p(X,\; \backslash Omega^q)\; \backslash Rightarrow\; H^(X,\; \backslash mathbf\; C)$ where ''X'' is a complex manifold, $H^(X,\; \backslash mathbf\; C)$ is its cohomology with complex coefficients and the left hand term, which is the $E\_2$-page of the spectral sequence, is the cohomology with values in the sheaf of holomorphic differential forms. The existence of the spectral sequence as stated above follows from the Poincaré lemma, which gives a quasi-isomorphism of complexes of sheaves :$\backslash mathbf\; C\; \backslash rightarrow\; \backslash Omega^$ * := (\stackrel d \to \Omega^1 \stackrel d \to \cdots \to \Omega^ ), together with the usual spectral sequence resulting from a filtered object, in this case the ''Hodge filtration'' : $F^p\; \backslash Omega^$ * := (\to 0 \to \Omega^p \to \Omega^ \to \cdots ) of $\backslash Omega^$ *. 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「Hodge–de Rham spectral sequence」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.