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Analytic $p$-adic cell decomposition and integrals

Author: Raf Cluckers
Journal: Trans. Amer. Math. Soc. 356 (2004), 1489-1499
MSC (2000): Primary 11S80, 32P05, 32B20; Secondary 03C10, 03C98, 11U09, 11S40
Published electronically: October 29, 2003
MathSciNet review: 2034315
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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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Additional Information

Raf Cluckers
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Address at time of publication: École Normale Supérieure, Département de Mathématiques et Applications, 45 rue d’Ulm, 75230 Paris Cedex 05, France

Keywords: Subanalytic $p$-adic sets, cell decomposition, $p$-adic integrals, Igusa's local zeta functions
Received by editor(s): August 15, 2002
Published electronically: October 29, 2003
Additional Notes: The author is a Research Assistant of the Fund for Scientific Research – Flanders (Belgium)(F.W.O.)
Article copyright: © Copyright 2003 American Mathematical Society

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