The $abcd$ conjecture, uniform boundedness, and dynamical systems
Number Theory
2024-04-24 v2 Algebraic Geometry
Dynamical Systems
Abstract
We survey Vojta's higher-dimensional generalizations of the conjecture and Szpiro's conjecture as well as recent developments that apply them to various problems in arithmetic dynamics. In particular, the " conjecture" implies a dynamical analogue of a conjecture on the uniform boundedness of torsion points and a dynamical analogue of Lang's conjecture on lower bounds for canonical heights.
Cite
@article{arxiv.2206.09725,
title = {The $abcd$ conjecture, uniform boundedness, and dynamical systems},
author = {Robin Zhang},
journal= {arXiv preprint arXiv:2206.09725},
year = {2024}
}
Comments
17 page, minor typo fixes