Notes on the dual of the ideal class groups of CM-fields

研究成果: Article査読

抄録

In this paper, for a CM abelian extension K/k of number fields, we propose a conjecture which describes completely the Fitting ideal of the minus part of the Pontryagin dual of the T-ray class group of K for a set T of primes as a Gal(K/k)-module. Here, we emphasize that we consider the full class group, and do not throw away the ramifying primes (the object we study is not the quotient of the class group by the subgroup generated by the classes of ramifying primes). We prove that our conjecture is a consequence of the equivariant Tamagawa number conjecture, and also prove the Iwasawa theoretic version of our conjecture.

本文言語English
ページ(範囲)971-996
ページ数26
ジャーナルJournal de Theorie des Nombres de Bordeaux
33
3.2
DOI
出版ステータスPublished - 2021

ASJC Scopus subject areas

  • 代数と数論

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