Applications of p-Adic Analysis for Bounding Periods of Subvarieties Under Etale Maps

Using methods of p-adic analysis, we obtain effective bounds for the length of the orbit of a preperiodic subvariety Y⊂ X under the action of an etale endomorphism of X. As a corollary of our result, we obtain effective bounds for the size of torsion of any semiabelian variety over a finitely generated field of characteristic 0. Our method allows us to show that any finitely generated torsion subgroup of Aut(X) is finite. This yields a different proof of Burnside’s problem for automorphisms of quasiprojective varieties X defined over a field of characteristic 0.