# Tate sequences and Fitting ideals of Iwasawa modules

@article{Greither2016TateSA, title={Tate sequences and Fitting ideals of Iwasawa modules}, author={Cornelius Greither and Masato Kurihara}, journal={St Petersburg Mathematical Journal}, year={2016}, volume={27}, pages={941-965} }

We consider abelian CM extensions L/k of a totally real field k, and we essentially determine the Fitting ideal of the dualized Iwasawa module studied by the second author [Ku3] in the case that only places above p ramify. In doing so we recover and generalise results of loc. cit. Remarkably, our explicit description of the Fitting ideal, apart from the contribution of the usual Stickelberger element Θ at infinity, only depends on the group structure of the Galois group Gal(L/k) and not on the…

## 8 Citations

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

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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,…

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The main conjectures in Iwasawa theory predict the relationship between the Iwasawa modules and the $p$-adic $L$-functions. Using a certain proved formulation of the main conjecture, Greither and…

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We describe classical and recent results concerning the structure of class groups of number fields as modules over the Galois group. When presenting more modern developments, we can only hint at the…

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Let K/k be a finite abelian CM-extension and T a suitable finite set of finite primes of k. In this paper, we determine the Fitting ideal of the minus component of the T -ray class group of K, except…

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Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois…

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We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using…

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For a finite abelian $p$-extension $K/k$ of totally real fields and the cyclotomic $\mathbb{Z}_{p}$-extension $K_{\infty}/K$, we prove a strong version of an equivariant Iwasawa main conjecture by…

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