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

@inproceedings{Cluckers2019UniformYP,
  title={Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields},
  author={Raf Cluckers and Arthur Forey and Franccois Loeser},
  year={2019}
}
— We prove a uniform version of non-Archimedean YomdinGromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result allows us to bound the number of Fq[t]-points of bounded degrees of algebraic varieties, uniformly in the cardinality q of the finite field Fq 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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