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Topics in Absolute Anabelian Geometry III: Global Reconsruction Algorithms
http://hdl.handle.net/2261/61285
http://hdl.handle.net/2261/61285a29151be-456d-4c0b-bab0-d3c0f2cad8e8
名前 / ファイル | ライセンス | アクション |
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jms220401.pdf (1.0 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2016-12-13 | |||||
タイトル | ||||||
タイトル | Topics in Absolute Anabelian Geometry III: Global Reconsruction Algorithms | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Absolute anabelian geometry | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | mono-anabelian | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | core | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Belyi cuspidalization | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | elliptic cuspidalization | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | arithmetic holomorphic structure | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | mono-analytic | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | log-Frobenius | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | log-shell | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | log-volume | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Mochizuki, Shinichi
× Mochizuki, Shinichi |
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著者所属 | ||||||
値 | Research Institute for Mathematical Sciences, Kyoto University | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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. | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 22, 号 4, p. 939-1156, 発行日 2015-12-10 |
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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 | |||||
日本十進分類法 | ||||||
主題Scheme | NDC | |||||
主題 | 415 | |||||
Mathematical Reviews Number | ||||||
値 | MR | |||||
Mathmatical Subject Classification | ||||||
値 | 14H30(MSC2010) | |||||
Mathmatical Subject Classification | ||||||
値 | 14H25(MSC2010) | |||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
値 | 2008-03-27 |