Analytic cell decomposition and analytic motivic integration |
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Authors: | Raf Cluckers |
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Institution: | Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200B, B-3001 Leuven, Belgium École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d'Ulm, 75230 Paris cedex 05, France1515Current address.; Purdue University, Department of Mathematics, West Lafayette, IN 47907-2067, USA; East Carolina University, Department of Mathematics, Greenville, NC 27858-4353, USA |
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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 Fq((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 motivique I, Comptes rendus de l'Académie des Sciences 339 (2004) 411-416]. |
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