Stickelberger ideals and Fitting ideals of class groups for abelian number fields

Masato Kurihara, Takashi Miura

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper, we determine completely the initial Fitting ideal of the minus part of the ideal class group of an abelian number field over Q up to the 2-component. This answers an open question of Mazur and Wiles (Invent Math 76:179-330, 1984) up to the 2-component, and proves Conjecture 0. 1 in Kurihara (J Reine Angew Math 561:39-86, 2003). We also study Brumer's conjecture and prove a stronger version for a CM-field, assuming certain conditions, in particular on the Galois group.

Original languageEnglish
Pages (from-to)549-575
Number of pages27
JournalMathematische Annalen
Volume350
Issue number3
DOIs
Publication statusPublished - 2011 Jul

ASJC Scopus subject areas

  • Mathematics(all)

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