Abstract
When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is the case, and conjecture precise conditions. 1. Asymptotic torsion Let be a lattice in a semisimple Lie group G. The asymptotic behaviour of the Betti numbers dimHj.; C/, when varies, has been studied by a number of authors. In particular, if N6 is a decreasing sequence of subgroups, with trivial intersection, the quotient
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