Analytic cell decomposition and analytic motivic integration
摘要
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 of big enough characteristic. To accomplish this, we introduce a general framework for Henselian valued fields with analytic structure, and we investigate the structure of analytic functions in one variable, defined on annuli over . 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 \emph{analytic} motivic integration and \emph{analytic} motivic constructible functions in the line of R. Cluckers and F. Loeser [\emph{Fonctions constructible et int\'egration motivic I}, Comptes rendus de l'Acad\'emie des Sciences, {\bf 339} (2004) 411 - 416].
引用
@article{arxiv.math/0503722,
title = {Analytic cell decomposition and analytic motivic integration},
author = {R. Cluckers and L. Lipshitz and Z. Robinson},
journal= {arXiv preprint arXiv:math/0503722},
year = {2007}
}