A note on finiteness of Tate cohomology groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916952300060672 |
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| author | Dhar, Sabyasachi Nadimpalli, Santosh |
| author_facet | Dhar, Sabyasachi Nadimpalli, Santosh |
| contents | Let $G$ be a reductive algebraic group defined over a non-Archimedean local field $F$ of residue characteristic $p$. Let $σ$ be an automorphism of $G$ of order $\ell$ -- a prime number -- with $\ell\neq p$. Let $Π$ be a finite length $\overline{\mathbb{F}}_\ell$-representation of $G(F)\rtimes \langleσ\rangle$. We show that the Tate cohomology $\widehat{H}^i(\langleσ\rangle, Π)$ is a finite length representation of $G^σ(F)$. We give an application to genericity of these Tate cohomology spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on finiteness of Tate cohomology groups Dhar, Sabyasachi Nadimpalli, Santosh Representation Theory Number Theory Let $G$ be a reductive algebraic group defined over a non-Archimedean local field $F$ of residue characteristic $p$. Let $σ$ be an automorphism of $G$ of order $\ell$ -- a prime number -- with $\ell\neq p$. Let $Π$ be a finite length $\overline{\mathbb{F}}_\ell$-representation of $G(F)\rtimes \langleσ\rangle$. We show that the Tate cohomology $\widehat{H}^i(\langleσ\rangle, Π)$ is a finite length representation of $G^σ(F)$. We give an application to genericity of these Tate cohomology spaces. |
| title | A note on finiteness of Tate cohomology groups |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2509.13297 |