Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure
Logic
2026-05-26 v4 Algebraic Geometry
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 -parametrized sets in Hensel minimal structures.
Cite
@article{arxiv.2505.19814,
title = {Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure},
author = {Krzysztof Jan Nowak},
journal= {arXiv preprint arXiv:2505.19814},
year = {2026}
}