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Homology of affine Springer fibers in the unramified case
Mark Goresky, Robert Kottwitz, and Robert MacPherson
Source: Duke Math. J. Volume 121, Number 3 (2004), 509-561.
Abstract
Assuming a certain "purity" conjecture, we derive a formula for the (complex) cohomology groups of the affine Springer fiber corresponding to any unramified regular semisimple element. We use this calculation to present a complex analog of the fundamental lemma for function fields. We show that the "kappa" orbital integral that arises in the fundamental lemma is equal to the Lefschetz trace of the Frobenius acting on the étale cohomology of a related variety.
Primary Subjects: 14M15, 11D88, 11F85
Secondary Subjects: 55N91
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1078170758
Digital Object Identifier: doi:10.1215/S0012-7094-04-12135-9
Mathematical Reviews number (MathSciNet):
MR2040285
Zentralblatt MATH identifier:
02067032
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