Analytic p-adic Cell Decomposition and Integrals

Details Analytic p-adic Cell Decomposition and Integrals Analytic p-adic Cell Decomposition and Integrals

2002-06-17

arxiv.org/abs/math/0206161v4

Trans. Amer. Math. Soc. 356 (2004), no. 4, 1489 --1499

Mathematics

Number Theory

The paper is accepted for publication in TAMS. Definitions 4.1 and 4.3 changed, making the integral operator $I$ zero if the p

Scientific paper

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 subanalytic sets up to subanalytic bijection.

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