English

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 abcabc conjecture and Szpiro's conjecture as well as recent developments that apply them to various problems in arithmetic dynamics. In particular, the "abcdabcd 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.

Keywords

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

R2 v1 2026-06-24T11:57:11.007Z