| 书目名称 | Noncommutative Iwasawa Main Conjectures over Totally Real Fields | | 副标题 | Münster, April 2011 | | 编辑 | John Coates,Peter Schneider,Otmar Venjakob | | 视频video | | | 概述 | Includes a self-contained and simplified proof of Kakde‘s main algebraic result, as well as introductory articles on related topics.Extremely useful for many years to come.Will almost certainly lead t | | 丛书名称 | Springer Proceedings in Mathematics & Statistics | | 图书封面 |  | | 描述 | The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developed in the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered an important idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde‘s proof is a beautiful development of these ideas of Kato, combined with an idea of Burns, and essentially redu | | 出版日期 | Conference proceedings 2013 | | 关键词 | 11R23, 11S40, 14H52, 14K22, 19B28; Iwasawa theory; K_1 of Iwasawa algebras; internal group logarithm; p- | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-32199-3 | | isbn_softcover | 978-3-642-44335-0 | | isbn_ebook | 978-3-642-32199-3Series ISSN 2194-1009 Series E-ISSN 2194-1017 | | issn_series | 2194-1009 | | copyright | Springer-Verlag Berlin Heidelberg 2013 |
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发表于 2025-3-21 16:52:34
