Applications of p-adic analysis for bounding periods of subvarieties under etale maps

Using methods of p-adic analysis we give a different proof of Burnside's problem for automorphisms of quasiprojective varieties X defined over a field of characteristic 0. More precisely, we show that any finitely generated torsion subgroup of Aut(X) is finite. In particular this yields effective bounds for the size of torsion of any semiabelian variety over a finitely generated field of characteristic 0. More precisely, we obtain effective bounds for the length of the orbit of a preperiodic subvariety under the action of an etale map.