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

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.

References in corpus (2)

• Some properties of analytic difference fields
• A non-archimedean Ax-Lindemann theorem

Cited by in corpus (8)

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• The dimension growth conjecture, polynomial in the degree and without logarithmic factors
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• A Pila--Wilkie theorem for Hensel minimal curves
• Improvements on dimension growth results and effective Hilbert's irreducibility theorem
• Rational points of rigid-analytic sets: a Pila-Wilkie type theorem
• Tame topology in Hensel minimal structures
• From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting