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arXiv · 2505.19814

Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure

Krzysztof Jan Nowak
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Abstract

The paper concerns uniform Yomdin-Gromov parametrizations together with an estimate of their number, which generalizes a theorem by Cluckers-Forey-Loeser to arbitrary equicharacteristic zero valued fields with analytic structure. To this end, we establish a certain strong analytic stratification of definable sets, based on a definable non-Archimedean version of Bierstone-Milman's canonical desingularization algorithm from our earlier paper. Other basic tools are: elimination of valued field quantifiers, term description of functions definable in analytic structures, and Lipschitz cell decomposition compatible with $RV$-parametrized sets in Hensel minimal structures.

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BibTeXRIS

Krzysztof Jan Nowak. 2025-05-26. Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure. https://arxiv.org/abs/2505.19814

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