Tate sequences and Fitting ideals of Iwasawa modules

C. Greither, M. Kurihara

研究成果: Article査読


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.

ジャーナルSt. Petersburg Mathematical Journal
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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