The asymptotic behaviour of the torsion in the cohomology of arithmetic groups

We will study the asymptotics of the torsion in the cohomology
of certain arithmetic groups with coefficients in certain Z-modules
if the rank of the Z-modules tends to infinity. Our first main result is
that for cocompact groups the torsion grows exponentially where the
leading term is proportional to the volume of the underlying locally
symmetric space. Our method is based on studying the analytic torsion of
locally symmetric spaces with coefficients in flat vector bundles. If these space
are no longer compact but only of finite volume, we will define a certain analog of
the analytic torsion, the so called regularized analytic torsion, and discuss  some
extensions of our results to the non-compact setting.