Analytic 𝑝-adic cell decomposition and integrals

Cluckers, Raf

doi:10.1090/S0002-9947-03-03458-5

Analytic $p$-adic cell decomposition and integrals
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by Raf Cluckers

Trans. Amer. Math. Soc. 356 (2004), 1489-1499

DOI: https://doi.org/10.1090/S0002-9947-03-03458-5

Published electronically: October 29, 2003

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Abstract:

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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