Determining class groups as Galois modules up to equivalence for some nonabelian extensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909746799312896 |
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| author | Greither, Cornelius Kataoka, Takenori |
| author_facet | Greither, Cornelius Kataoka, Takenori |
| contents | In previous papers, the Galois module structure of minus class groups was studied for abelian CM extensions. In this paper, we discuss some nonabelian cases, focusing on metacyclic extensions. For a certain class of these, we obtain a complete description of the Galois modules that occur as minus class groups, modulo a certain equivalence relation on modules, which was introduced earlier by the same authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determining class groups as Galois modules up to equivalence for some nonabelian extensions Greither, Cornelius Kataoka, Takenori Number Theory In previous papers, the Galois module structure of minus class groups was studied for abelian CM extensions. In this paper, we discuss some nonabelian cases, focusing on metacyclic extensions. For a certain class of these, we obtain a complete description of the Galois modules that occur as minus class groups, modulo a certain equivalence relation on modules, which was introduced earlier by the same authors. |
| title | Determining class groups as Galois modules up to equivalence for some nonabelian extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.15242 |