Exponential growth of torsion in Abelian coverings

We study the growth of the order of torsion subgroups of the homology in a tower of finite abelian coverings. In particular, we prove that it is exponential for when the tower converges to the maximal free abelian cover of a link complement when the first nonzero Alexander polynomial has positive logarithmic Mahler measure.
Comment: 42 pages, to appear in AGT. Various minor mistakes corrected and exposition changed