Tate sequences and Fitting ideals of Iwasawa modules

C. Greither, M. Kurihara

研究成果: Article査読

抄録

We consider Abelian CM extensions L/k of a totally real field k, and we essentially determine the Fitting ideal of the dualized Iwasawa module studied by the second author in the case where only places above p ramify. In doing so we recover and generalize the results mentioned above. Remarkably, our explicit description of the Fitting ideal, apart from the contribution of the usual Stickelberger element Θ˙ at infinity, only depends on the group structure of the Galois group Gal(L/k) and not on the specific extension L. From our computation it is then easy to deduce that T˙Θ˙ is not in the Fitting ideal as soon as the p-part of Gal(L/k) is not cyclic. We need a lot of technical preparations: resolutions of the trivial module ℤ over a group ring, discussion of the minors of certain big matrices that arise in this context, and auxiliary results about the behavior of Fitting ideals in short exact sequences.

本文言語English
ページ(範囲)941-965
ページ数25
ジャーナルSt. Petersburg Mathematical Journal
27
6
DOI
出版ステータスPublished - 2016

ASJC Scopus subject areas

  • 分析
  • 代数と数論
  • 応用数学

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