Modular perverse sheaves on flag varieties II: Koszul duality and formality
arXiv:1401.7256 · doi:10.1215/00127094-3165541
Abstract
Building on the theory of parity sheaves due to Juteau-Mautner-Williamson, we develop a formalism of "mixed modular perverse sheaves" for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a "Koszul-type" derived equivalence relating a given flag variety to the Langlands dual flag variety, and (2) a formality theorem for the modular derived category of a flag variety (extending a previous result of Riche-Soergel-Williamson).
40 pages. v2: minor revisions