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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 Chevalley scheme ： ウィキペディア英語版 Chevalley scheme A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory. Let ''X'' be a separated integral noetherian scheme, ''R'' its function field. If we denote by $X\text{'}$ the set of subrings $\backslash mathcal\; O\_x$ of ''R'', where ''x'' runs through ''X'' (when $X=\backslash mathrm(A)$, we denote $X\text{'}$ by $L(A)$), $X\text{'}$ verifies the following three properties * For each $M\backslash in\; X\text{'}$, ''R'' is the field of fractions of ''M''. * There is a finite set of noetherian subrings $A\_i$ of ''R'' so that $X\text{'}=\backslash cup\_i\; L(A\_i)$ and that, for each pair of indices ''i,j'', the subring $A\_$ of ''R'' generated by $A\_i\; \backslash cup\; A\_j$ is an $A\_i$-algebra of finite type. * If $M\backslash subseteq\; N$ in $X\text{'}$ are such that the maximal ideal of ''M'' is contained in that of ''N'', then ''M=N''. Originally, Chevalley also supposed that R was an extension of finite type of a field K and that the $A\_i$'s were algebras of finite type over a field too (this simplifies the second condition above). ==Bibliography== * (Online ) 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「Chevalley scheme」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.