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Journal Articles Duke Mathematical Journal Year : 2015

Modular perverse sheaves on flag varieties II: Koszul duality and formality

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).
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Dates and versions

hal-00938001 , version 1 (29-01-2014)
hal-00938001 , version 2 (06-02-2015)

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Pramod N. Achar, Simon Riche. Modular perverse sheaves on flag varieties II: Koszul duality and formality. Duke Mathematical Journal, 2015, ⟨10.1215/00127094-3165541⟩. ⟨hal-00938001v2⟩
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