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.
Publication Source (Journal or Book title)
International Mathematics Research Notices
Achar, P., & Kitchen, S. (2014). Koszul duality and mixed hodge modules. International Mathematics Research Notices, 2014 (21), 5874-5911. https://doi.org/10.1093/imrn/rnt148