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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Definable sets, motives and $p$-adic integrals


Authors: Jan Denef and François Loeser
Journal: J. Amer. Math. Soc. 14 (2001), 429-469
MSC (2000): Primary 03C10, 03C98, 12E30, 12L12, 14G15, 14G20, 14G27; Secondary 11G25, 11S40, 12L10, 14F20, 14G05, 14G10, 14J20
Published electronically: December 8, 2000
MathSciNet review: 1815218
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Abstract: We associate a canonical virtual motive to definable sets over a field of characteristic zero. We use this construction to show that very general $p$-adic integrals are canonically interpolated by motivic ones.


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Additional Information

Jan Denef
Affiliation: Department of Mathematics, University of Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Email: Jan.Denef@wis.kuleuven.ac.be

François Loeser
Affiliation: Département de mathématiques et applications, École Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France (UMR 8553 du CNRS)
Email: Francois.Loeser@ens.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-00-00360-X
PII: S 0894-0347(00)00360-X
Received by editor(s): October 6, 1999
Received by editor(s) in revised form: October 20, 2000
Published electronically: December 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society