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 "Koszultype" 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).
Publication Source (Journal or Book title)
Duke Mathematical Journal
Achar, P., & Riche, S. (2016). Modular perverse sheaves on flag varieties, II: Koszul duality and formality. Duke Mathematical Journal, 165 (1), 161-215. https://doi.org/10.1215/00127094-3165541