Analytic cell decomposition and analytic motivic integration

By Raf Cluckers, Leonard Lipshitz, Z. Robinson. 2005

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Abstract 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 F q ( ( 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 integration motivique I , Comptes rendus de l'Academie des Sciences 339 (2004) 411–416].

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/51726b79cbc163f75092f0ed4d7bf5fb725efe64