Sur l'homologie des fibres de Springer affines tronquées

Details Sur l'homologie des fibres de Springer affines tronquées Sur l'homologie des fibres de Springer affines tronquées

2007-02-20

arxiv.org/abs/math/0702586v1

Mathematics

Algebraic Geometry

77 pages

Scientific paper

Following Goresky, Kottwitz and MacPherson, we compute the homology of truncated affine Springer fibers in the unramified case but under a purity assumption. We prove this assumption in the equivalued case. The truncation parameter is viewed as a divisor on an l-adic toric variety. For each fiber, we introduce a graded quasi-coherent sheaf on the toric variety whose space of global sections is precisely the l-adic homology of the truncated affine Springer fiber. Moreover, for some families of endoscopic groups, these sheaves show up in an exact sequence. As a consequence we prove Arthur's weighted fundamental lemma in the unramified equivalued case.

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