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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.21681 |
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| _version_ | 1866917357870383104 |
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| author | Chitrao, Anand Karnataki, Aditya Ray, Jishnu |
| author_facet | Chitrao, Anand Karnataki, Aditya Ray, Jishnu |
| contents | Let $S$ be a Banach algebra over $\mathbb{Q}_p$ whose residue fields are finite extensions of $\mathbb{Q}_p$. Given an arithmetic family $V$ of Galois representations, i.e., a finite free $S$-module $V$ with a continuous action of the absolute Galois group of a $p$-adic number field, we construct a complex associated to $V$ over false-Tate extensions and construct explicit isomorphisms between its cohomology and the Galois cohomology. This recovers earlier results by Tavares Ribeiro when $S$ is a finite extension of $\mathbb{Q}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21681 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit isomorphisms for a Herr-type complex over a metabelian extension Chitrao, Anand Karnataki, Aditya Ray, Jishnu Number Theory Representation Theory 11F80, 11S25, 14F30 Let $S$ be a Banach algebra over $\mathbb{Q}_p$ whose residue fields are finite extensions of $\mathbb{Q}_p$. Given an arithmetic family $V$ of Galois representations, i.e., a finite free $S$-module $V$ with a continuous action of the absolute Galois group of a $p$-adic number field, we construct a complex associated to $V$ over false-Tate extensions and construct explicit isomorphisms between its cohomology and the Galois cohomology. This recovers earlier results by Tavares Ribeiro when $S$ is a finite extension of $\mathbb{Q}_p$. |
| title | Explicit isomorphisms for a Herr-type complex over a metabelian extension |
| topic | Number Theory Representation Theory 11F80, 11S25, 14F30 |
| url | https://arxiv.org/abs/2603.21681 |