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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 Essentially finite vector bundle ： ウィキペディア英語版 Essentially finite vector bundle In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav Nori,〔M. V. Nori ''On the Representations of the Fundamental Group'', Compositio Mathematica, Vol. 33, Fasc. 1, (1976), p. 29–42〕〔T. Szamuely ''Galois Groups and Fundamental Groups.'' Cambridge Studies in Advanced Mathematics, Vol. 117 (2009)〕 as the main tool in the construction of the fundamental group scheme. Even if the definition is not intuitive there is a nice characterization that makes essentially finite vector bundles quite natural objects to study in algebraic geometry. So before recalling the definition we give this characterization: ==Characterization== Let $X$ be a reduced and connected scheme over a perfect field $k$ endowed with a section $x\backslash in\; X(k)$. Then a vector bundle $V$ over $X$ is essentially finite if and only if there exists a finite $k$-group scheme $G$ and a $G$-torsor $p:P\backslash to\; X$ such that $V$ becomes trivial over $P$ (i.e. $p^$ *(V)\cong O_P^, where $r=rk(V)$). 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「Essentially finite vector bundle」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.