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

Masato Kurihara, Takashi Miura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2012 Dec

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Ideal class groups of CM-fields with non-cyclic galois action'. Together they form a unique fingerprint.

Cite this