The Uniform Boundedness and Dynamical Lang Conjectures for polynomials
Number Theory
2025-12-23 v3 Dynamical Systems
Abstract
We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical analogue of Lang's conjecture on minimal canonical heights for these maps. We obtain similar results for non-isotrivial polynomials over a function field of characteristic zero. When the latter are unicritical of degree at least 5, the results hold unconditionally.
Cite
@article{arxiv.2105.05240,
title = {The Uniform Boundedness and Dynamical Lang Conjectures for polynomials},
author = {Nicole R. Looper},
journal= {arXiv preprint arXiv:2105.05240},
year = {2025}
}