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

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Abstract

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.

Original languageEnglish
Pages (from-to)971-996
Number of pages26
JournalJournal de Theorie des Nombres de Bordeaux
Volume33
Issue number3.2
DOIs
Publication statusPublished - 2021

Keywords

  • Class groups, Fitting ideals
  • Mots-clefs

ASJC Scopus subject areas

  • Algebra and Number Theory

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