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March 2017 Fitting Ideals of Iwasawa Modules and of the Dual of Class Groups
Cornelius GREITHER, Masato KURIHARA
Tokyo J. Math. 39(3): 619-642 (March 2017). DOI: 10.3836/tjm/1475723094

Abstract

In this paper we study some problems related to a refinement of Iwasawa theory, especially questions about the Fitting ideals of several natural Iwasawa modules and of the dual of the class groups, as a sequel to our previous papers [8], [3]. Among other things, we prove that the annihilator of $\mathbb{Z}_{p}(1)$ times the Stickelberger element is not in the Fitting ideal of the dualized Iwasawa module if the $p$-component of the bottom Galois group is elementary $p$-abelian with $p$-rank $\geq 4$. Our results can be applied to the case that the base field is $\mathbb{Q}$.

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Cornelius GREITHER. Masato KURIHARA. "Fitting Ideals of Iwasawa Modules and of the Dual of Class Groups." Tokyo J. Math. 39 (3) 619 - 642, March 2017. https://doi.org/10.3836/tjm/1475723094

Information

Published: March 2017
First available in Project Euclid: 6 October 2016

zbMATH: 06727279
MathSciNet: MR3634286
Digital Object Identifier: 10.3836/tjm/1475723094

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 3 • March 2017
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