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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 Rosati involution ： ウィキペディア英語版 Rosati involution In mathematics, a Rosati involution, named after Carlo Rosati, is an involution of the rational endomorphism ring of an abelian variety induced by a polarization. Let $A$ be an abelian variety, let $\backslash hat\; A=\backslash mathrm^0(A)$ be the dual abelian variety, and for $a\backslash in\; A$, let $T\_a:A\backslash to\; A$ be the translation-by-$a$ map, $T\_a(x)=x+a$. Then each divisor $D$ on $A$ defines a map $\backslash phi\_D:A\backslash to\backslash hat\; A$ via . The map $\backslash phi\_D$ is a polarization, i.e., has finite kernel, if and only if $D$ is ample. The Rosati involution of $\backslash mathrm(A)\backslash otimes\backslash mathbb$ relative to the polarization $\backslash phi\_D$ sends a map $\backslash psi\backslash in\backslash mathrm(A)\backslash otimes\backslash mathbb$ to the map $\backslash psi\text{'}=\backslash phi\_D^\backslash circ\backslash hat\backslash psi\backslash circ\backslash phi\_D$, where $\backslash hat\backslash psi:\backslash hat\; A\backslash to\backslash hat\; A$ is the dual map induced by the action of $\backslash psi^$ * on $\backslash mathrm(A)$. Let $\backslash mathrm(A)$ denote the Néron–Severi group of $A$. The polarization $\backslash phi\_D$ also induces an inclusion $\backslash Phi:\backslash mathrm(A)\backslash otimes\backslash mathbb\backslash to\backslash mathrm(A)\backslash otimes\backslash mathbb$ via $\backslash Phi\_E=\backslash phi\_D^\backslash circ\backslash phi\_E$. The image of $\backslash Phi$ is equal to $\backslash :\backslash psi\text{'}=\backslash psi\backslash \}$, i.e., the set of endomorphisms fixed by the Rosati involution. The operation $E\backslash star\; F=\backslash frac12\backslash Phi^(\backslash Phi\_E\backslash circ\backslash Phi\_F+\backslash Phi\_F\backslash circ\backslash Phi\_E)$ then gives $\backslash mathrm(A)\backslash otimes\backslash mathbb$ the structure of a formally real Jordan algebra. ==References== * * 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「Rosati involution」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.