翻訳と辞書 Words near each other ・ Artine Artinian ・ Artines ・ Artington ・ Artinian ・ Artinian ideal ・ Artinian module ・ Artinian ring ・ Artinite ・ Artins ・ ArtInsights ・ Artinskian ・ Artinsky District ・ Artin–Hasse exponential ・ Artin–Mazur zeta function ・ Artin–Rees lemma ・ Artin–Schreier curve ・ Artin–Schreier theory ・ Artin–Tate lemma ・ Artin–Verdier duality ・ Artin–Wedderburn theorem ・ Artin–Zorn theorem ・ Artio ・ Artio Films ・ Artiocetus ・ Artiom Gaiduchevici ・ Artiom Haceaturov ・ Artiom Kiouregkian ・ Artion Poçi ・ Artiora ・ ArtiosCAD Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Artin–Schreier curve ： ウィキペディア英語版 Artin–Schreier curve In mathematics, an Artin–Schreier curve is a plane curve defined over an algebraically closed field of characteristic $p$ by an equation :$y^p\; -\; y\; =\; f(x)$ for some rational function $f$ over that field. One of the most important examples of such curves is hyperelliptic curves in characteristic 2, whose Jacobian varieties have been suggested for use in cryptography. It is common to write these curves in the form :$y^2\; +\; h(x)\; y\; =\; f(x)$ for some polynomials $f$ and $h$. == Definition == More generally, an ''Artin-Schreier curve'' defined over an algebraically closed field of characteristic $p$ is a branched covering :$C\; \backslash to\; \backslash mathbb^1$ of the projective line of degree $p$. Such a cover is necessarily cyclic, that is, the Galois group of the corresponding algebraic function field extension is the cyclic group $\backslash mathbb/p\backslash mathbb$. In other words, $k(C)/k(x)$ is an Artin–Schreier extension. The fundamental theorem of Artin–Schreier theory implies that such a curve defined over a field $k$ has an affine model :$y^p\; -\; y\; =\; f(x),$ for some rational function $f\; \backslash in\; k(x)$ that is not equal for $z^p\; -\; z$ for any other rational function $z$. In other words, if we define polynomial $g(z)\; =\; z^p\; -\; z$, then we require that $f\; \backslash in\; k(x)\; \backslash backslash\; g(k(x))$. 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「Artin–Schreier curve」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.