Projective Surface Automorphisms of Positive Topological Entropy from an Arithmetic Viewpoint

Let X be a smooth projective surface over a number field K([inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i"/] C), 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 ĥ_D corresponding to a certain nef and big R-divisor D on X and transforming well relative to f, and deduce some arithmetic properties of f-periodic points and non f-periodic points.