{"created":"2021-03-01T06:59:30.668309+00:00","id":39955,"links":{},"metadata":{"_buckets":{"deposit":"7b882171-a1aa-4b82-a3d2-9ba9aa27c1e1"},"_deposit":{"id":"39955","owners":[],"pid":{"revision_id":0,"type":"depid","value":"39955"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00039955","sets":["312:6865:6873:6874","9:504:6868:6875:6876"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2015-12-10","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"4","bibliographicPageEnd":"1156","bibliographicPageStart":"939","bibliographicVolumeNumber":"22","bibliographic_titles":[{"bibliographic_title":"Journal of mathematical sciences, the University of Tokyo"}]}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"In the present paper, which forms the third part of a three-part series on an algorithmic approach to absolute anabelian geometry, we apply the absolute anabelian technique of Belyi cuspidalization developed in the second part, together with certain ideas contained in an earlier paper of the author concerning the categorytheoretic representation of holomorphic structures via either the topological group SL2(R) or the use of “parallelograms, rectangles, and squares”, to develop a certain global formalism for certain hyperbolic orbicurves related to a once-punctured elliptic curve over a number field. This formalism allows one to construct certain canonical rigid integral structures, which we refer to as log-shells, that are obtained by applying the logarithm at various primes of a number field. Moreover, although each of these local logarithms is “far from being an isomorphism” b oth in the sense that it fails to respect the ring structures involved and in the sense (cf. Frobenius morphisms in positive characteristic!) that it has the effect of exhibiting the “mass”represen ted by its domain as a “somewhat smaller collection of mass” than the “mass”represen ted by its codomain, this global formalism allows one to treat the logarithm operation as a global operation on a number field which satisfies the property of being an “isomomorphism up to an appropriate renormalization operation”, in a fashion that is reminiscent of the isomorphism induced on differentials by a Frobenius lifting, once one divides by p. More generally, if one thinks of number fields as corresponding to positive characteristic hyperbolic curves and of once-punctured elliptic curves on a number field as corresponding to nilpotent ordinary indigenous bundles on a positive characteristic hyperbolic curve, then many aspects of the theory developed in the present paper are reminiscent of (the positive characteristic portion of) p-adic Teichm¨uller theory.","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":"MR"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"14H30(MSC2010)"},{"subitem_text_value":"14H25(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2008-03-27"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Research Institute for Mathematical Sciences, Kyoto University"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Mochizuki, Shinichi"}],"nameIdentifiers":[{"nameIdentifier":"92361","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":"2017-06-14"}],"displaytype":"detail","filename":"jms220401.pdf","filesize":[{"value":"1.0 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms220401.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/39955/files/jms220401.pdf"},"version_id":"50ec4430-45ec-4a1a-94c3-de4043809e15"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Absolute anabelian geometry","subitem_subject_scheme":"Other"},{"subitem_subject":"mono-anabelian","subitem_subject_scheme":"Other"},{"subitem_subject":"core","subitem_subject_scheme":"Other"},{"subitem_subject":"Belyi cuspidalization","subitem_subject_scheme":"Other"},{"subitem_subject":"elliptic cuspidalization","subitem_subject_scheme":"Other"},{"subitem_subject":"arithmetic holomorphic structure","subitem_subject_scheme":"Other"},{"subitem_subject":"mono-analytic","subitem_subject_scheme":"Other"},{"subitem_subject":"log-Frobenius","subitem_subject_scheme":"Other"},{"subitem_subject":"log-shell","subitem_subject_scheme":"Other"},{"subitem_subject":"log-volume","subitem_subject_scheme":"Other"}]},"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":"Topics in Absolute Anabelian Geometry III: Global Reconsruction Algorithms","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Topics in Absolute Anabelian Geometry III: Global Reconsruction Algorithms"}]},"item_type_id":"4","owner":"1","path":["6874","6876"],"pubdate":{"attribute_name":"公開日","attribute_value":"2016-12-13"},"publish_date":"2016-12-13","publish_status":"0","recid":"39955","relation_version_is_last":true,"title":["Topics in Absolute Anabelian Geometry III: Global Reconsruction Algorithms"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:14:44.322349+00:00"}