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arXiv · 1902.06589

Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields

Raf Cluckers·Arthur Forey·François Loeser
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Abstract

We prove a uniform version of non-Archimedean Yomdin-Gromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result allows us to bound the number of F_q[t]-points of bounded degrees of algebraic varieties, uniformly in the cardinality q of the finite field F_q and the degree, generalizing work by Sedunova for fixed q. We also deduce a uniform non-Archimedean Pila-Wilkie theorem, generalizing work by Cluckers-Comte-Loeser.

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Raf Cluckers, Arthur Forey, François Loeser. 2019-02-18. Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields. https://doi.org/10.2140/ant.2020.14.1423

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