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15 February 2004 Homology of affine Springer fibers in the unramified case
Mark Goresky, Robert Kottwitz, Robert MacPherson
Duke Math. J. 121(3): 509-561 (15 February 2004). DOI: 10.1215/S0012-7094-04-12135-9

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.

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Mark Goresky. Robert Kottwitz. Robert MacPherson. "Homology of affine Springer fibers in the unramified case." Duke Math. J. 121 (3) 509 - 561, 15 February 2004. https://doi.org/10.1215/S0012-7094-04-12135-9

Information

Published: 15 February 2004
First available in Project Euclid: 1 March 2004

zbMATH: 1162.14311
MathSciNet: MR2040285
Digital Object Identifier: 10.1215/S0012-7094-04-12135-9

Subjects:
Primary: 11D88, 11F85, 14M15
Secondary: 55N91

Rights: Copyright © 2004 Duke University Press

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Vol.121 • No. 3 • 15 February 2004
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