  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.
