Lower Bounds for Galois Orbits of periodic points for polarized endomorphisms

Jit Wu Yap; Tien-Cuong Dinh

paper

Lower Bounds for Galois Orbits of periodic points for polarized endomorphisms

arXiv:2512.02343

Abstract

Let $K$ be a number field, $X$ a smooth projective variety over $K$ and $f : X \to X$ a polarized endomorphism of degree $d \geq 2$ . We prove an exponential lower bound on $[K(\Per_n):K]$, where $\Per_n$ is the set of $n$ -periodic points, extending results of [Yap24] to higher dimensions. We also prove a quantitative rate of equidistribution for $\Per_n$ to the equilibrium measure.