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arXiv · 2508.09114

Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms

Jason P. Bell·Thomas J. Tucker
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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.

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BibTeXRIS

Jason P. Bell, Thomas J. Tucker. 2025-08-12. Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms. https://arxiv.org/abs/2508.09114

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