2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124299Following 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.77 pagesAlgebraic GeometryRepresentation Theory14F20, 14F63, 22E67, 11F70text