Rubin-Stark elements and ideal class groups (Algebraic Number Theory and Related Topics 2013)

栗原, 将人

説明

This article is a survey of the Galois module structure of the class groups of number fields, and of their relation with the L-values. After we explain several classical results, e.g., the order of a character component of a class group, etc., we introduce the Rubin-Stark conjecture in Rubin [27], which asserts the existence of certain algebraic elements related to the L-values. We also explain some new properties of Rubin-Stark elements obtained in a joint work of the author with D. Burns and T. Sano [7], including the description of the Fitting ideals of class groups and certain cohomology groups. We also give several concrete examples.

収録刊行物

数理解析研究所講究録別冊

数理解析研究所講究録別冊 B53 343-363, 2015-09

Research Institute for Mathematical Sciences, Kyoto University

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詳細情報詳細情報について

CRID: 1050564288205503488

NII論文ID: 110010033675

NII書誌ID: AA12196120

ISSN: 18816193

HANDLE: 2433/241292

本文言語コード: en

資料種別: departmental bulletin paper

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