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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 Groupoid scheme ： ウィキペディア英語版 Groupoid scheme In algebraic geometry, a groupoid scheme is a pair of schemes $R,\; U$ together with five morphisms $s,\; t:\; R\; \backslash to\; U,\; e:\; U\; \backslash to\; R,\; m:\; R\; \backslash times\_\; R\; \backslash to\; R,\; i:\; R\; \backslash to\; R$ satisfying $s\; \backslash circ\; e,\; t\; \backslash circ\; e$ are the identity morphisms, $s\; \backslash circ\; m\; =\; s\; \backslash circ\; p\_1,\; t\; \backslash circ\; m\; =\; t\; \backslash circ\; p\_2$ and other obvious conditions that generalize the axioms of group action; e.g., associativity. In practice, it is usually written as $R\; \backslash rightrightarrows\; U$ (cf. coequalizer.) Example: Suppose an algebraic group ''G'' acts from the right on a scheme ''U''. Then take $R\; =\; U\; \backslash times\; G$, ''s'' the projection, ''t'' the given action. The main use of the notion is that it provides an atlas for a stack. More specifically, let $(\backslash rightrightarrows\; U)$ be the category of $(R\; \backslash rightrightarrows\; U)$-torsors. Then it is a category fibered in groupoids; in fact, a Deligne–Mumford stack. Conversely, any DM stack is of this form. == Notes == 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「Groupoid 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.