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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Orbital integrals are motivic

Author: Thomas C. Hales
Journal: Proc. Amer. Math. Soc. 133 (2005), 1515-1525
MSC (2000): Primary 22E50
Published electronically: December 15, 2004
MathSciNet review: 2111953
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Abstract: This article shows that under general conditions, $p$-adic orbital integrals of definable functions are represented as the trace of a Frobenius operator on a virtual motive. This gives an explicit example of the philosophy of Denef and Loeser, which predicts that all ``naturally occurring'' $p$-adic integrals are motivic.

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Additional Information

Thomas C. Hales
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

PII: S 0002-9939(04)07740-8
Received by editor(s): January 7, 2002
Received by editor(s) in revised form: October 24, 2003
Published electronically: December 15, 2004
Additional Notes: This research was supported by NSF grant 245332
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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