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arXiv · 2210.12784

On the top-dimensional cohomology of arithmetic Chevalley groups

Benjamin Brück·Yuri Santos Rego·Robin J. Sroka
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Abstract

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 T\'oth on Steinberg modules to prove that $H^{\operatorname{vcd}}(\mathcal{G}(\mathfrak{O}); \mathbb{Q}) = 0$ if $\mathfrak{O}$ is Euclidean.

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Benjamin Brück, Yuri Santos Rego, Robin J. Sroka. 2022-10-23. On the top-dimensional cohomology of arithmetic Chevalley groups. https://doi.org/10.1090/proc/16948

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