Uniform bounds for the number of rational points on varieties over global fields
Number Theory
2023-03-29 v4 Algebraic Geometry
Abstract
We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the factor by a factor.
Keywords
Cite
@article{arxiv.2101.12174,
title = {Uniform bounds for the number of rational points on varieties over global fields},
author = {Marcelo Paredes and Román Sasyk},
journal= {arXiv preprint arXiv:2101.12174},
year = {2023}
}
Comments
v4: final version. Fixed some typos and errors pointed out by the referee. To appear in Algebra and Number Theory. 45 pages