On the growth of torsion in the cohomology of arithmetic groups

TL;DR

This paper investigates the exponential growth of torsion in the cohomology of specific arithmetic groups, providing insights into their algebraic and geometric properties.

Contribution

It demonstrates that torsion in the cohomology of certain arithmetic groups grows exponentially with natural sequences of modules, a novel finding in this context.

Findings

Torsion growth is exponential in studied families.

Focus on arithmetic subgroups of SO^0(p,q) and SL_3(R).

Provides new understanding of cohomological torsion behavior.

Abstract

In this paper we consider certain families of arithmetic subgroups of SO^0(p,q) and SL_3(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.