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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 Closed immersion ： ウィキペディア英語版 Closed immersion :''For the same-name concept in differential geometry, see immersion (mathematics).'' In algebraic geometry, a closed immersion of schemes is a morphism of schemes $f:\; Z\; \backslash to\; X$ that identifies ''Z'' as a closed subset of ''X'' such that regular functions on ''Z'' can be extended locally to ''X''.〔Mumford, ''The Red Book of Varieties and Schemes'', Section II.5〕 The latter condition can be formalized by saying that $f^\backslash \#:\backslash mathcal\_X\backslash rightarrow\; f\_\backslash ast\backslash mathcal\_Z$ is surjective. An example is the inclusion map $\backslash operatorname(R/I)\; \backslash to\; \backslash operatorname(R)$ induced by the canonical map $R\; \backslash to\; R/I$. ==Other characterizations== The following are equivalent: #$f:\; Z\; \backslash to\; X$ is a closed immersion. #For every open affine $U\; =\; \backslash operatorname(R)\; \backslash subset\; X$, there exists an ideal $I\; \backslash subset\; R$ such that $f^(U)\; =\; \backslash operatorname(R/I)$ as schemes over ''U''. #There exists an open affine covering $X\; =\; \backslash bigcup\; U\_j,\; U\_j\; =\; \backslash operatorname\; R\_j$ and for each ''j'' there exists an ideal $I\_j\; \backslash subset\; R\_j$ such that $f^(U\_j)\; =\; \backslash operatorname\; (R\_j\; /\; I\_j)$ as schemes over $U\_j$. #There is a quasi-coherent sheaf of ideals $\backslash mathcal$ on ''X'' such that $f\_\backslash ast\backslash mathcal\_Z\backslash cong\; \backslash mathcal\_X/\backslash mathcal$ and ''f'' is an isomorphism of ''Z'' onto the global Spec of $\backslash mathcal\_X/\backslash mathcal$ over ''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「Closed immersion」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.