Groups, Geometry, and Dynamics


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Volume 10, Issue 1, 2016, pp. 91–115
DOI: 10.4171/GGD/344

Published online: 2016-02-09

An infinitely generated virtual cohomology group for noncocompact arithmetic groups over function fields

Kevin Wortman

Let ${\bf G} (\mathcal{O}_S)$ be a noncocompact irreducible arithmetic group over a global function field $K$ of characteristic $p$, and let $\Gamma$ be a finite-index, residually $p$-finite subgroup of ${\bf G}(\mathcal{O}_S)$. We show that the cohomology of $\Gamma$ in the dimension of its associated Euclidean building with coefficients in the field of $p$ elements is infinite.

Keywords: Cohomology of groups, arithmetic groups, Euclidean buildings

Wortman Kevin: An infinitely generated virtual cohomology group for noncocompact arithmetic groups over function fields. Groups Geom. Dyn. 10 (2016), 91-115. doi: 10.4171/GGD/344