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.
Citation
Marcelo Paredes. Román Sasyk. "Uniform bounds for the number of rational points on varieties over global fields." Algebra Number Theory 16 (8) 1941 - 2000, 2022. https://doi.org/10.2140/ant.2022.16.1941
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