NON-ARCHIMEDEAN YOMDIN-GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT

@inproceedings{Cluckers2015NONARCHIMEDEANYP,
  title={NON-ARCHIMEDEAN YOMDIN-GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT},
  author={Raf Cluckers and Georges Comte and Franccois Loeser},
  year={2015}
}
We prove an analog of the Yomdin–Gromov lemma for p-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected case. We apply this result to bound the number of rational points of bounded height on the transcendental part of p-adic subanalytic sets, and to bound the dimension of the set of complex polynomials of bounded degree lying on an algebraic variety… CONTINUE READING

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