Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms
Number Theory
2025-08-13 v1 Algebraic Geometry
Abstract
In this paper, we explore a variety of finiteness questions for preperiodic points of morphisms. We begin by treating a group action analog of the Burnside problem for torsion groups using the p-adic arc method. We then prove some results connecting commonality of preperiodic points for elements of an automorphism group with structural properties of the group; these results are related to well-known results of Tits and Borel. We finish by proving some Northcott-type results for finite morphisms.
Cite
@article{arxiv.2508.09114,
title = {Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms},
author = {Jason P. Bell and Thomas J. Tucker},
journal= {arXiv preprint arXiv:2508.09114},
year = {2025}
}
Comments
11 pages