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

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Description

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.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B53 343-363, 2015-09

    Research Institute for Mathematical Sciences, Kyoto University

Keywords

Details 詳細情報について

  • CRID
    1050564288205503488
  • NII Article ID
    110010033675
  • NII Book ID
    AA12196120
  • ISSN
    18816193
  • HANDLE
    2433/241292
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB
    • CiNii Articles

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