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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 Fundamental group scheme ： ウィキペディア英語版 Fundamental group scheme In mathematics, the fundamental group scheme is a group scheme canonically associated to a scheme over a Dedekind scheme (e.g. the spectrum of a field or the spectrum of a discrete valuation ring). It is a generalisation of the étale fundamental group. Although its existence was conjectured by Alexander Grothendieck, the first construction is due to 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)〕 who only worked on schemes over fields. A generalisation to schemes over Dedekind schemes is due to Carlo Gasbarri.〔C. Gasbarri, ''Heights of Vector Bundles and the Fundamental Group Scheme of a Curve'', Duke Mathematical Journal, Vol. 117, No. 2, (2003) p. 287-311〕 ==First definition== Let $k$ be a perfect field and $X\backslash to\; \backslash text(k)$ a faithfully flat and proper morphism of schemes with $X$ a reduced and connected scheme. Assume the existence of a section $x:\backslash text(k)\backslash to\; X$, then the fundamental group scheme $\backslash pi\_1(X,x)$ of $X$ in $x$ is defined as the affine group scheme naturally associated to the neutral tannakian category (over $k$) of essentially finite vector bundles 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「Fundamental group 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.