Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties

TL;DR

This paper proves a conjecture relating to the growth rates of points under self-morphisms of semi-abelian varieties, establishing key properties of their arithmetic and dynamical degrees.

Contribution

It confirms Kawaguchi-Silverman's conjecture for semi-abelian varieties and characterizes the set of possible arithmetic and dynamical degrees.

Findings

Proved the Kawaguchi-Silverman conjecture for semi-abelian varieties

Determined the set of arithmetic degrees of orbits

Identified the first dynamical degrees of self-morphisms

Abstract

We prove a conjecture by Kawaguchi-Silverman on arithmetic and dynamical degrees, for self-morphisms of semi-abelian varieties. Moreover, we determine the set of the arithmetic degrees of orbits and the (first) dynamical degrees of self-morphisms of semi-abelian varieties.