Building on the theory of parity sheaves due to Juteau, Mautner, and 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, and Williamson).
"Modular perverse sheaves on flag varieties, II: Koszul duality and formality." Duke Math. J. 165 (1) 161 - 215, 15 January 2016. https://doi.org/10.1215/00127094-3165541