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arXiv · 2101.12174

Uniform bounds for the number of rational points on varieties over global fields

Marcelo Paredes·Román Sasyk
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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 $4$ 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 $B^{\varepsilon}$ factor by a $\log(B)$ factor.

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Marcelo Paredes, Román Sasyk. 2021-11-12. Uniform bounds for the number of rational points on varieties over global fields. https://doi.org/10.2140/ant.2022.16.1941

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