Koszul duality and mixed hodge modules

Abstract

We prove that on a certain class of smooth complex varieties (those with affine even stratifications ), the category of mixed Hodge modules is almost Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give an equivalence between perverse sheaves on such a variety and modules for a certain graded ring, obtaining a formality result as a corollary. For flag varieties, these results were proved earlier by Beilinson-Ginzburg-Soergel using a rather different construction