On the top-dimensional cohomology of arithmetic Chevalley groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912418296233984 |
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| author | Brück, Benjamin Rego, Yuri Santos Sroka, Robin J. |
| author_facet | Brück, Benjamin Rego, Yuri Santos Sroka, Robin J. |
| contents | Let $\mathbb{K}$ be a number field with ring of integers $\mathfrak{O}$ and let $\mathcal{G}$ be a Chevalley group scheme not of type $\mathtt{E}_8$, $\mathtt{F}_4$ or $\mathtt{G}_2$. We use the theory of Tits buildings and a result of Tóth on Steinberg modules to prove that $H^{\operatorname{vcd}}(\mathcal{G}(\mathfrak{O}); \mathbb{Q}) = 0$ if $\mathfrak{O}$ is Euclidean. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12784 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the top-dimensional cohomology of arithmetic Chevalley groups Brück, Benjamin Rego, Yuri Santos Sroka, Robin J. Algebraic Topology Group Theory Number Theory 11F75, 20E42, 57M07 Let $\mathbb{K}$ be a number field with ring of integers $\mathfrak{O}$ and let $\mathcal{G}$ be a Chevalley group scheme not of type $\mathtt{E}_8$, $\mathtt{F}_4$ or $\mathtt{G}_2$. We use the theory of Tits buildings and a result of Tóth on Steinberg modules to prove that $H^{\operatorname{vcd}}(\mathcal{G}(\mathfrak{O}); \mathbb{Q}) = 0$ if $\mathfrak{O}$ is Euclidean. |
| title | On the top-dimensional cohomology of arithmetic Chevalley groups |
| topic | Algebraic Topology Group Theory Number Theory 11F75, 20E42, 57M07 |
| url | https://arxiv.org/abs/2210.12784 |