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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 sheaf of modules ： ウィキペディア英語版 sheaf of modules In mathematics, a sheaf of ''O''-modules or simply an ''O''-module over a ringed space (''X'', ''O'') is a sheaf ''F'' such that, for any open subset ''U'' of ''X'', ''F''(''U'') is an ''O''(''U'')-module and the restriction maps ''F''(''U'') →''F''(''V'') are compatible with the restriction maps ''O''(''U'') →''O''(''V''): the restriction of ''fs'' is the restriction of ''f'' times that of ''s'' for any ''f'' in ''O''(''U'') and ''s'' in ''F''(''U''). The standard case is when ''X'' is a scheme and ''O'' its structure sheaf. If ''O'' is the constant sheaf $\backslash underline^i(X,\; -)$ as the ''i''-th right derived functor of the global section functor $\backslash Gamma(X,\; -)$.〔This cohomology functor coincides with the right derived functor of the global section functor in the category of abelian sheaves; cf. 〕 == Examples == *If ''F'' is an ''O''-module, then an ''O''-submodule of ''F'' is called the ideal or ideal sheaf of ''O''. *Let ''X'' be a smooth variety of dimension ''n''. Then the tangent sheaf of ''X'' is the dual of the cotangent sheaf $\backslash Omega\_X$ and the canonical sheaf $\backslash omega\_X$ is the ''n''-th exterior power (determinant) of $\backslash Omega\_X$. 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「sheaf of modules」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.