Lower Bounds for Galois Orbits of periodic points for polarized endomorphisms

Jit Wu Yap; Tien-Cuong Dinh

Lower Bounds for Galois Orbits of periodic points for polarized endomorphisms

Number Theory 2025-12-03 v1 Dynamical Systems

Authors: Jit Wu Yap , Tien-Cuong Dinh

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.

Keywords

Galois orbits periodic points polarized endomorphisms equidistribution exponential lower bound

Cite

@article{arxiv.2512.02343,
  title  = {Lower Bounds for Galois Orbits of periodic points for polarized endomorphisms},
  author = {Jit Wu Yap and Tien-Cuong Dinh},
  journal= {arXiv preprint arXiv:2512.02343},
  year   = {2025}
}

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