{"created":"2021-03-01T06:59:59.307025+00:00","id":40375,"links":{},"metadata":{"_buckets":{"deposit":"6214d918-2b3b-4bb8-bb1a-b5f30faa7f94"},"_deposit":{"id":"40375","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40375"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040375","sets":["312:6865:7071:7077","9:504:6868:7073:7078"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1994","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"136","bibliographicPageStart":"71","bibliographicVolumeNumber":"1","bibliographic_titles":[{"bibliographic_title":"Journal of mathematical sciences, the University of Tokyo"}]}]},"item_4_description_13":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"415","subitem_subject_scheme":"NDC"}]},"item_4_text_16":{"attribute_name":"Mathematical Reviews Number","attribute_value_mlt":[{"subitem_text_value":"MR1298541"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"14E20(MSC1991)"},{"subitem_text_value":"14F35(MSC1991)"},{"subitem_text_value":"20F34(MSC1991)"},{"subitem_text_value":"20F36(MSC1991)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"1992-03-10"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Nakamura, Hiroaki"}],"nameIdentifiers":[{"nameIdentifier":"138973","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-06-27"}],"displaytype":"detail","filename":"jms010103.pdf","filesize":[{"value":"442.2 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms010103.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40375/files/jms010103.pdf"},"version_id":"29ec6cc3-3ecd-421f-bcbe-45171e70ccc6"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Galois rigidity of pure sphere braid groups and profinite calculus","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Galois rigidity of pure sphere braid groups and profinite calculus"}]},"item_type_id":"4","owner":"1","path":["7077","7078"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40375","relation_version_is_last":true,"title":["Galois rigidity of pure sphere braid groups and profinite calculus"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:44.122671+00:00"}