Homology of affine Springer fibers in the unramified case
Goresky, Mark ; Kottwitz, Robert ; MacPherson, Robert
Duke Math. J., Tome 121 (2004) no. 1, p. 509-561 / Harvested from Project Euclid
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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.
Publié le : 2004-02-15
Classification:  14M15,  11D88,  11F85,  55N91 
@article{1078170758,
     author = {Goresky, Mark and Kottwitz, Robert and MacPherson, Robert},
     title = {Homology of affine Springer fibers in the unramified case},
     journal = {Duke Math. J.},
     volume = {121},
     number = {1},
     year = {2004},
     pages = { 509-561},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1078170758}
}

Goresky, Mark; Kottwitz, Robert; MacPherson, Robert. Homology of affine Springer fibers in the unramified case. Duke Math. J., Tome 121 (2004) no. 1, pp.  509-561. http://gdmltest.u-ga.fr/item/1078170758/