Analytic cell decomposition and analytic motivic integration
| dc.creator | Cluckers, R. | |
| dc.creator | Lipshitz, L. | |
| dc.creator | Robinson, Z. | |
| dc.date | 2005-03-31 | |
| dc.date.accessioned | 2026-07-07T05:18:39Z | |
| dc.date.available | 2026-07-07T05:18:39Z | |
| dc.description | 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 $\FF_q((t))$ 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 \emph{analytic} motivic integration and \emph{analytic} motivic constructible functions in the line of R. Cluckers and F. Loeser [\emph{Fonctions constructible et intégration motivic I}, Comptes rendus de l'Académie des Sciences, {\bf 339} (2004) 411 - 416]. | |
| dc.identifier | https://arxiv.org/abs/math/0503722 | |
| dc.identifier | http://arxiv.org/abs/math/0503722 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74738 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 32P05; 32B05; 32B20; 03C10; 28B10 | |
| dc.title | Analytic cell decomposition and analytic motivic integration | |
| dc.type | text |