Koszul duality and mixed Hodge modules
Representation Theory
2013-03-20 v4 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1105.2181,
title = {Koszul duality and mixed Hodge modules},
author = {Pramod N. Achar and S. Kitchen},
journal= {arXiv preprint arXiv:1105.2181},
year = {2013}
}
Comments
26 pages. v4: added Proposition 3.9; streamlined Section 4; other minor corrections