  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.
