On the Galois module structure of minus class groups

Cornelius Greither; Takenori Kataoka

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arXiv · 2404.11823

On the Galois module structure of minus class groups

Cornelius Greither·Takenori Kataoka

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Abstract

The main object of this paper is the minus class groups associated to CM-fields as Galois modules. In a previous article of the authors, we introduced a notion of equivalence for modules and determined the equivalence classes of the minus class groups. In this paper, we show a concrete application of this result. We also study how large a proportion of equivalence classes can be realized as classes of minus class groups.

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Cornelius Greither, Takenori Kataoka. 2024-04-18. On the Galois module structure of minus class groups. https://arxiv.org/abs/2404.11823

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