On stronger versions of brumer’s conjecture

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3 Citations (Scopus)

Abstract

Let k be a totally real number field and L a CM-field such that L/k is finite and abelian. In this paper, we study a stronger version of Brumer’s conjecture that the Stickelberger element times the annihilator of the group of roots of unity in L is in the Fitting ideal of the ideal class group of L, and also study the dual version. We mainly study the Teichmüller character component, and determine the Fitting ideal in a certain case. We will see that these stronger versions hold in a certain case. It is known that the stronger version (SB) does not hold in general. We will prove in this paper that the dual version (DSB) does not hold in general, either.

Original languageEnglish
Pages (from-to)407-428
Number of pages22
JournalTokyo Journal of Mathematics
Volume34
Issue number2
DOIs
Publication statusPublished - 2017

ASJC Scopus subject areas

  • Mathematics(all)

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