Regulator Constants and Cohomology
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912935090061312 |
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| author | Caputo, Luca |
| author_facet | Caputo, Luca |
| contents | We show how regulator constants of a finitely generated $\mathbb{Z}[G]$-module can be related to $G$-cohomology, where $G$ is a finite group. We then derive consequences of such relation for modules naturally arising in number theory, such as ring of integers and units of number fields, $K$-theory groups of ring of integers and Mordell-Weil groups of elliptic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regulator Constants and Cohomology Caputo, Luca Number Theory Representation Theory 11R33 (Primary) 20C10, 11R34, 11R29, 11R20, 11R70, 11G05 (Secondary) We show how regulator constants of a finitely generated $\mathbb{Z}[G]$-module can be related to $G$-cohomology, where $G$ is a finite group. We then derive consequences of such relation for modules naturally arising in number theory, such as ring of integers and units of number fields, $K$-theory groups of ring of integers and Mordell-Weil groups of elliptic curves. |
| title | Regulator Constants and Cohomology |
| topic | Number Theory Representation Theory 11R33 (Primary) 20C10, 11R34, 11R29, 11R20, 11R70, 11G05 (Secondary) |
| url | https://arxiv.org/abs/2603.01310 |