Zariski density of points with maximal arithmetic degree for surfaces

TL;DR

This paper proves that for certain self-morphisms on smooth projective surfaces over number fields, the set of rational points with maximal arithmetic degree is dense, indicating rich arithmetic structure.

Contribution

It establishes the density of rational points with maximal arithmetic degree for surjective self-morphisms with elta_f > 1 on smooth projective surfaces over number fields.

Findings

Densely many L-rational points with maximal arithmetic degree exist for these surfaces.

Surjective self-morphisms with elta_f > 1 have dense rational points.

The result applies to potentially dense surfaces over number fields.

Abstract

We prove that any surjective self-morphism with $\delta_f > 1$ on a potentially dense smooth projective surface defined over a number field $K$ has densely many $L$-rational points for a finite extension $L/K$.