Tokyo Journal of Mathematics

Fitting Ideals of Iwasawa Modules and of the Dual of Class Groups

Cornelius GREITHER and Masato KURIHARA

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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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Tokyo J. Math., Volume 39, Number 3 (2017), 619-642.

First available in Project Euclid: 6 October 2016

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GREITHER, Cornelius; KURIHARA, Masato. Fitting Ideals of Iwasawa Modules and of the Dual of Class Groups. Tokyo J. Math. 39 (2017), no. 3, 619--642. doi:10.3836/tjm/1475723094.

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