Orbit Transversality for Abelian Varieties

Abstract

Let $X/K$ be an abelian variety defined over a number field and let $f:X\to X$ be a dominant morphism defined over $K$. We show that $(f,K)$ is strongly dense orbit transversal. That is, up to replacing $K$ with a finite extension, every set of representatives for grand $(f,K)$-orbits is Zariski dense in $X$.