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.Comment: 26 pages. v4: added Proposition 3.9; streamlined Section 4; other
minor correction
