Homology of affine Springer fibers in the unramified case

Preprint

9 May 2003

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0305144

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 semi-simple element. We use this calculation to present a complex analog of the fundamental lemma for function fields. We show that the "kappa" orbital integral which arises in the fundamental lemma is equal to the Lefschetz trace of Frobenius acting on the etale cohomology of a related variety.

Keywords

AFFINE SPRINGER FIBERS
SPRINGER FIBERS
UNRAMIFIED CASE
CASE ASSUMING
COHOMOLOGY
LEMMA

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Version 1, 2003-05-09, ArXiv

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