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Galois rigidity of pure sphere braid groups and profinite calculus
http://hdl.handle.net/2261/1590
http://hdl.handle.net/2261/1590ff2239da-57b3-470d-b70c-5f3ee8bb18c8
名前 / ファイル | ライセンス | アクション |
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jms010103.pdf (442.2 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2008-03-04 | |||||
タイトル | ||||||
タイトル | Galois rigidity of pure sphere braid groups and profinite calculus | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Nakamura, Hiroaki
× Nakamura, Hiroaki |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Let $\frak C$ be a class of finite groups closed under the formation of subgroups, quotients, and group extensions. For an algebraic variety $X$ over a number field $k$, let $π^{\frak C}_1(X)$ denote the ($\frak C$-modified) profinite fundamental group of $X$ having the absolute Galois group $Gal(\bar k/k)$ as a quotient with kernel $π^{\frak C}_1(X_{\bar k})$ the maximal pro-$\frak C$ quotient of the geometric fundamental group of $X$. The purpose of this paper is to show certain rigidity properties of $π^{\frak C}_1(X)$ for $X$ of hyperbolic type through the study of outer automorphism group $Outπ^{\frak C}_1(X)$ of $π^{\frak C}_1(X)$. In particular, we show finiteness of $Outπ^{\frak C}_1(X)$ when $X$ is a certain typical hyperbolic variety and $\frak C$ is the class of finite $l$-groups ($l$: odd prime). Indeed, we have a criterion of Gottlieb type for center-triviality of $π^{\frak C}_1(X_{\bar k})$ under certain good hyperbolicity condition on $X$. Then our question on finiteness of $Outπ^{\frak C}_1(X)$ for such $X$ is reduced to the study of the exterior Galois representation $\varphi^{\frak C}_X:Gal(\bar k/k)\to Outπ^{\frak C}_1(X_{\bar k})$, especially to the estimation of the centralizer of the Galois image of $\varphi^{\frak C}_X$ (\S 1.6). In \S 2, we study the case where $X$ is an algebraic curve of hyperbolic type, and give fundamental tools and basic results. We devote \S 3, \S 4 and Appendix to detailed studies of the special case $X=M_{0, n}$, the moduli space of the $n$-point punctured projective lines $(n\ge 3)$, which are closely related with topological work of N. V. Ivanov, arithmetic work of P. Delinge, Y. Ihara, and categorical work of V. G. Drinfeld. Section 4 deal with a Lie variant suggested by P. Deligne. | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 1, 号 1, p. 71-136, 発行日 1994 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題 | 415 | |||||
主題Scheme | NDC | |||||
Mathematical Reviews Number | ||||||
MR1298541 | ||||||
Mathmatical Subject Classification | ||||||
14E20(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
14F35(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
20F34(MSC1991) | ||||||
Mathmatical Subject Classification | ||||||
20F36(MSC1991) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
1992-03-10 |