2005/03/31 by Raf Cluckers, R. Cluckers, Leonard Lipshitz +6 · 1 citation
Mathematics · #03C10 #28B10 #32B05 #32B20 #32P05 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Rings, Modules, and Algebras #math.AG #math.NT #msc:03C10 #msc:28B10 #msc:32B05 #msc:32B20 #msc:32P05
paper · pdf · doi:10.48550/arxiv.math/0503722
arxiv created 2005/03/31 · openalex publication_date 2005/03/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef-Pas language, and its application to analytic motivic integrals and analytic integrals over \FFq((t)) of big enough characteristic. To accomplish this, we introduce a general framework for Henselian valued fields K with analytic structure, and we investigate the structure of analytic functions in one variable, defined on annuli over K. We also prove that, after parameterization, definable analytic functions are given by terms. The results in this paper pave the way for a theory of analytic motivic integration and analytic motivic constructible functions in the line of R. Cluckers and F. Loeser [Fonctions constructible et intégration motivic I, Comptes rendus de l'Académie des Sciences, \bf 339 (2004) 411 - 416].