Arithmetic hyperbolicity: automorphisms and persistence

Abstract We show that if the automorphism group of a projective variety is torsion, then it finite. Motivated by Lang’s conjecture on rational points hyperbolic varieties, we use this to prove with only finitely many has automorphisms. Moreover, investigate what extent finiteness S -integral over number field persists generated fields. To end, introduce class mildly bounded varieties and general criterion for proving persistence.