English

On the top-dimensional cohomology of arithmetic Chevalley groups

Algebraic Topology 2025-06-10 v2 Group Theory Number Theory

Abstract

Let K\mathbb{K} be a number field with ring of integers O\mathfrak{O} and let G\mathcal{G} be a Chevalley group scheme not of type E8\mathtt{E}_8, F4\mathtt{F}_4 or G2\mathtt{G}_2. We use the theory of Tits buildings and a result of T\'oth on Steinberg modules to prove that Hvcd(G(O);Q)=0H^{\operatorname{vcd}}(\mathcal{G}(\mathfrak{O}); \mathbb{Q}) = 0 if O\mathfrak{O} is Euclidean.

Keywords

Cite

@article{arxiv.2210.12784,
  title  = {On the top-dimensional cohomology of arithmetic Chevalley groups},
  author = {Benjamin Brück and Yuri Santos Rego and Robin J. Sroka},
  journal= {arXiv preprint arXiv:2210.12784},
  year   = {2025}
}

Comments

8 pages; v2: small changes according to referee's suggestions; to appear in Proc. Amer. Math. Soc