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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Definable sets, motives and $p$-adic integrals
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by Jan Denef and François Loeser PDF
J. Amer. Math. Soc. 14 (2001), 429-469 Request permission


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:
  • François Loeser
  • Affiliation: Département de mathématiques et applications, École Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France (UMR 8553 du CNRS)
  • MR Author ID: 115300
  • ORCID: 0000-0002-7065-5497
  • Email:
  • Received by editor(s): October 6, 1999
  • Received by editor(s) in revised form: October 20, 2000
  • Published electronically: December 8, 2000
  • © Copyright 2000 American Mathematical Society
  • 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
  • DOI:
  • MathSciNet review: 1815218