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 -points of bounded degrees of algebraic varieties, uniformly in the cardinality of the finite field and the degree, generalizing work by Sedunova for fixed . We also deduce a uniform non-Archimedean Pila–Wilkie theorem, generalizing work by Cluckers–Comte–Loeser.
Citation
Raf Cluckers. Arthur Forey. François Loeser. "Uniform Yomdin–Gromov parametrizations and points of bounded height in valued fields." Algebra Number Theory 14 (6) 1423 - 1456, 2020. https://doi.org/10.2140/ant.2020.14.1423
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