On the growth of torsion in the cohomology of arithmetic groups

Abstract

In this paper we consider certain families of arithmetic subgroups of $$\mathrm{SO }^0(p,q)$$ and $$\mathrm{SL }_3(\mathbb {R})$$ , respectively. We study the cohomology of such arithmetic groups with coefficients in arithmetically defined modules. We show that for natural sequences of such modules the torsion in the cohomology grows exponentially.