Ideal class groups of CM-fields with non-cyclic galois action

Masato Kurihara, Takashi Miura

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3 Citations (Scopus)

Abstract

Suppose that L/k is a finite and abelian extension such that k is a totally real base field and L is a CM-field. We regard the ideal class group Cl L, of L as a Gal(L/k)-module. As a sequel of the paper [8] by the first author, we study a problem whether the Stickelberger element for L/k times the annihilator ideal of the roots of unity in L is in the Fitting ideal of ClL, and also a problem whether it is in the Fitting ideal of the Pontrjagin dual (ClL)v. We systematically construct extensions L/k for which these properties do not hold, and also give numerical examples.

Original languageEnglish
Pages (from-to)411-439
Number of pages29
JournalTokyo Journal of Mathematics
Volume35
Issue number2
DOIs
Publication statusPublished - 2012 Dec 1

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ASJC Scopus subject areas

  • Mathematics(all)

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