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  1. 121 数理科学研究科
  2. Journal of Mathematical Sciences, the University of Tokyo
  3. 20
  4. 2
  1. 0 資料タイプ別
  2. 30 紀要・部局刊行物
  3. Journal of Mathematical Sciences, the University of Tokyo
  4. 20
  5. 2

Topics in Absolute Anabelian Geometry II : Decomposition Groups and Endomorphisms

http://hdl.handle.net/2261/59041
http://hdl.handle.net/2261/59041
27e992c6-c3cd-4c2e-bccc-887c9ad3c291
名前 / ファイル ライセンス アクション
jms200201.pdf jms200201.pdf (572.7 kB)
Item type 紀要論文 / Departmental Bulletin Paper(1)
公開日 2015-12-15
タイトル
タイトル Topics in Absolute Anabelian Geometry II : Decomposition Groups and Endomorphisms
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 hyperbolic curves
キーワード
主題Scheme Other
主題 absolute p-adic Grothendieck Conjecture
キーワード
主題Scheme Other
主題 p-adic Section Conjecture
キーワード
主題Scheme Other
主題 configuration spaces
キーワード
主題Scheme Other
主題 hidden endomorphisms
キーワード
主題Scheme Other
主題 point-theoreticity
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
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ departmental bulletin paper
著者 Mochizuki, Shinichi

× Mochizuki, Shinichi

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Mochizuki, Shinichi

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著者所属
著者所属 Research Institute for Mathematical Sciences, Kyoto University
抄録
内容記述タイプ Abstract
内容記述 The present paper, which forms the second part of a three-part series in which we study absolute anabelian geometry from an algorithmic point of view, focuses on the study of the closely related notions of decomposition groups and endomorphisms in this anabelian context. We begin by studying an abstract combinatorial analogue of the algebro-geometric notion of a stable polycurve (i.e., a “successive extension of families of stable curves”) and showing that the “geometry of log divisors on stable polycurves” may be extended, in a purely group-theoretic fashion, to this abstract combinatorial analogue; this leads to various anabelian results concerning configuration spaces. We then turn to the study of the absolute pro-Σ anabelian geometry of hyperbolic curves over mixed-characteristic local fields, for Σ a set of primes of cardinality ≥ 2 that contains the residue characteristic of the base field. In particular, we prove a certain “pro-p resolution of nonsingularities” type result, which implies a “conditional” anabelian result to the effect that the condition, on an isomorphism of arithmetic fundamental groups, of preservation of decomposition groups of “most” closed points implies that the isomorphism arises from an isomorphism of schemes — i.e., in a word, “point-theoreticity implies geometricity”; a “non-conditional” version of this result is then obtained for “procurves” obtained by removing from a proper curve some set of closed points which is “p-adically dense in a Galois-compatible fashion”. Finally, we study, from an algorithmic point of view, the theory of Belyi and elliptic cuspidalizations, i.e., group-theoretic reconstruction algorithms for the arithmetic fundamental group of an open subscheme of a hyperbolic curve that arise from consideration of certain endomorphisms determined by Belyi maps and endomorphisms of elliptic curves.
書誌情報 Journal of mathematical sciences, the University of Tokyo

巻 20, 号 2, p. 171-269, 発行日 2013-11-20
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
MR
Mathmatical Subject Classification
14H30(MSC2010)
Mathmatical Subject Classification
14H25(MSC2010)
出版者
出版者 Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
2008-03-26
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