An Infinite Dimensional Virtual Cohomology Group of ${\text{SL}}_3(\mathbb{Z}[t])$

Abstract

We prove that ${\text{SL}}_3(\mathbb{Z}[t])$ has a finite index subgroup $\Gamma$ such that $H^2(\Gamma ;\mathbb{Q})$ is infinite dimensional. The proof uses the geometry of the Euclidean building for ${\text{SL}}_3(\mathbb{Q}((t^{-1})))$.

References in corpus (1)

• Higher finiteness properties of reductive arithmetic groups in positive characteristic: the rank theorem