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Topics in Absolute Anabelian Geometry I : Generalities
http://hdl.handle.net/2261/55362
http://hdl.handle.net/2261/55362d2f48787-8bec-4494-bc6e-6727e17f18b0
名前 / ファイル | ライセンス | アクション |
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jms190201.pdf (604.4 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2013-09-10 | |||||
タイトル | ||||||
タイトル | Topics in Absolute Anabelian Geometry I : Generalities | |||||
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 |
Mochizuki, Shinichi
× 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 | This paper forms the first part of a three-part series in which we treat various topics in absolute anabelian geometry from the point of view of developing abstract algorithms, or "software", that may be applied to abstract profinite groups that "just happen" to arise as (quotients of) étale fundamental groups from algebraic geometry. One central theme of the present paper is the issue of understanding the gap between relative, "semi-absolute, and absolute anabelian geometry. We begin by studying various abstract combinatorial properties of profinite groups that typically arise as absolute Galois groups or arithmetic/geometric fundamental groups in the anabelian geometry of quite general varieties in arbitrary dimension over number fields, mixed-characteristic local fields, or finite fields. These considerations, combined with the classical theory of Albanese varieties, allow us to derive an absolute anabelian algorithm for constructing the quotient of an arithmetic fundamental group determined by the absolute Galois group of the base field in the case of quite general varieties of arbitrary dimension. Next, we take a more detailed look at certain p-adic Hodge-theoretic aspects of the absolute Galois groups of mixed-characteristic local fields. This allows us, for instance, to derive, from a certain result communicated orally to the author by A. Tamagawa, a "semi-absolute" Hom-version --- whose absolute analogue is false! --- of the anabelian conjecture for hyperbolic curves over mixed-characteristic local fields. Finally, we generalize to the case of varieties of arbitrary dimension over arbitrary sub-p-adic fields certain techniques developed by the author in previous papers over mixed-characteristic local fields for applying relative anabelian results to obtain "semi-absolute" group-theoretic contructions of the étale fundamental group of one hyperbolic curve from the étale fundamental group of another closely related hyperbolic curve. | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 19, 号 2, p. 139-242, 発行日 2012-09-10 |
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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 | 415 | |||||
主題Scheme | NDC | |||||
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 | ||||||
2008-03-27 |