Stratifications and term description over valued fields with analytic structure, uniform Yomdin-Gromov parametrizations

2025/05/26 by Nowak, Krzysztof Jan
#03C98 #14B05 #32S45 #32S60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2505.19814

Abstract

We establish a certain strong smooth stratification of sets and a term description of functions, which are definable over valued fields (possibly non algebraically closed) with analytic structure. The basic tools are: elimination of valued field quantifiers, term structure of definable functions, Lipschitz cell decomposition with preparation of RV-parametrized sets, and a non-Archimedean definable version of Bierstone-Milman's canonical desingularization algorithm, achieved in an earlier paper of ours. As application, uniform Yomdin-Gromov parametrizations of definable sets are given.

Citations

• Counting rational points on transcendental curves in valued fields
• Hensel minimality II: Mixed characteristic and a diophantine application
• The Yomdin-Gromov algebraic lemma revisited
• Complex Cellular Structures
• Uniform parameterization of subanalytic sets and diophantine applications
• Some results of algebraic geometry over Henselian rank one valued fields
• Strictly convergent analytic structures
• Continuous rational functions on real and p-adic varieties
• Functorial desingularization over Q: boundaries and the embedded case
• Fields with Analytic Structure
• Analytic cell decomposition and analytic motivic integration
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant

Related

• A Non-Archimedean Approach to Stratifications
• Lipschitz stratifications in power-bounded o-minimal fields
• Fields with Analytic Structure
• Arc-wise analytic t-stratifications
• Strictly convergent analytic structures