Vanishing of odd-dimensional intersection cohomology (Q1098903)

This vanishing of intersection cohomology sheaves with middle perversity is derived for projective varieties on which a linear group acts, under certain conditions such as that some one-parameter subgroup has only finitely many fixed points. The proof uses étale hypercohomology in the context of simplicial schemes and a criterion of Deligne for the degeneration of a Leray spectral sequence, discussed in an appendix.