Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Looper, Nicole R.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3162474933