Strong stratifications and uniform Yomdin-Gromov parametrizations in valued fields with analytic structure
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Nowak, Krzysztof Jan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891872797
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