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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 Base change map ： ウィキペディア英語版 Base change map In mathematics, the base change map relates the direct image and the pull-back of sheaves. More precisely, it is the following natural transformation of sheaves: :$g^$ *(R^r f_ * \mathcal) \to R^r f'_ *(g'^ *\mathcal) where $f:\; X\; \backslash to\; S,\; f\text{'}:X\text{'}\; \backslash to\; S\text{'},\; g\text{'}:X\text{'}\; \backslash to\; X,\; g:S\text{'}\; \backslash to\; S$ are continuous maps between topological spaces that form a Cartesian square and $\backslash mathcal$ is a sheaf on ''X''. In general topology, the map is an isomorphism under some mild technical conditions. An analogous result holds for étale cohomologies (with topological spaces replaced by sites), though more difficult. See proper base change theorem. == General topology == If ''X'' is a Hausdorff topological space, ''S'' is a locally compact Hausdorff space and ''f'' is universally closed (i.e., $X\; \backslash times\_S\; T\; \backslash to\; T$ is closed for any continuous map $T\; \backslash to\; S$), then the base change map is an isomorphism. Indeed, we have: for $s\; \backslash in\; S$, :$(R^r\; f\_$ * \mathcal)_s = \varinjlim H^r(U, \mathcal) = H^r(X_s, \mathcal), \quad X_s = f^(s) and so for $s\; =\; g(t)$ :$g^$ * (R^r f_ * \mathcal)_t = H^r(X_s, \mathcal) = H^r(X'_t, g'^ * \mathcal) = R^r f'_ * (g'^ * \mathcal)_t. 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「Base change map」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.