Analytic p-adic cell decomposition and integrals

By Raf Cluckers. 2002

59 citations recorded by the source corpus.

We prove a conjecture of Denef on parameterized p-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 silbanalytic sets up to subanalytic bijection.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1f05dedacb01aac54f433f1e8d2c2dc3438937d6

Citations in the corpus

• Constructible exponential functions, motivic Fourier transform and transfer principle (2005, unknown): “In the p-adic semialgebraic case, cell decomposition theorems are due to Cohen [12] and Denef [14], [16] and they were extended in [4] to the subanalytic setting where one can find the following version:”
• Fields with analytic structure (2009, unknown): “Cluckers: Laboratoire Painlevé, CNRS - UMR 8524, Université Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq Cedex, France, and Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium; e-mail: raf.cluckers@wis.kuleuven.be; URL: www.wis.kuleuven.be/”