Analytic p-adic Cell Decomposition and Integrals
Number Theory
2007-05-23 v4 Logic
Abstract
We prove a conjecture of Denef on parameterized -adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalytic bijection.
Cite
@article{arxiv.math/0206161,
title = {Analytic p-adic Cell Decomposition and Integrals},
author = {Raf Cluckers},
journal= {arXiv preprint arXiv:math/0206161},
year = {2007}
}
Comments
The paper is accepted for publication in TAMS. Definitions 4.1 and 4.3 changed, making the integral operator $I$ zero if the parametrized function is not integrable for all parameters, where as before it was zero only in those parameters where the function is not integrable