Resumen de Projective surface automorphisms of positive topological entropy from an arithmetic viewpoint

Shu Kawaguchi

• Let X be a smooth projective surface over a number field K ( ? ), and f: X ? X an automorphism of positive topological entropy. In this paper, we show that there are only finitely many f-periodic curves on X. Then we define a height function corresponding to a certain nef and big -divisor D on X and transforming well relative to f, and deduce some arithmetic properties of f-periodic points and non f-periodic points.