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Preprint Number 1568

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1568. Raf Cluckers and Arthur Forey and François Loeser
Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields

Submission date: 18 February 2019


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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Full text arXiv 1902.06589: pdf, ps.

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