Homology of affine Springer fibers in the unramified case

Details Homology of affine Springer fibers in the unramified case Homology of affine Springer fibers in the unramified case

2003-05-09

arxiv.org/abs/math/0305144v1

Mathematics

Representation Theory

Scientific paper

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.

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