On the Galois module structure of minus class groups

2024/04/18 by Cornélius Greither, Greither, Cornelius, Takenori Kataoka +1 · 1 citation
Mathematics · #11R29 (Primary) 11R33 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2404.11823

openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Determining class groups as Galois modules up to equivalence for some nonabelian extensions

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