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December 2011 On Stronger Versions of Brumer's Conjecture
Masato KURIHARA
Tokyo J. Math. 34(2): 407-428 (December 2011). DOI: 10.3836/tjm/1327931394

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.

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Masato KURIHARA. "On Stronger Versions of Brumer's Conjecture." Tokyo J. Math. 34 (2) 407 - 428, December 2011. https://doi.org/10.3836/tjm/1327931394

Information

Published: December 2011
First available in Project Euclid: 30 January 2012

zbMATH: 1270.11117
MathSciNet: MR2918914
Digital Object Identifier: 10.3836/tjm/1327931394

Rights: Copyright © 2011 Publication Committee for the Tokyo Journal of Mathematics

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Vol.34 • No. 2 • December 2011
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