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Journal Articles Compositio Mathematica Year : 2013

Modular Koszul duality

Abstract

We prove an analogue of Koszul duality for category O of a reductive group G in positive characteristic p larger than 1 plus the number of roots of G. However there are no Koszul rings, and we do not prove an analogue of the Kazhdan--Lusztig conjectures in this context. The main technical result is the formality of the dg-algebra of extensions of parity sheaves on the flag variety if the characteristic of the coefficients is at least the number of roots of G plus 2.
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Dates and versions

hal-00733191 , version 1 (18-09-2012)

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Simon Riche, Wolfgang Soergel, Geordie Williamson. Modular Koszul duality. Compositio Mathematica, 2013, ⟨10.1112/S0010437X13007483⟩. ⟨hal-00733191⟩
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