Modular Koszul duality

Simon Riche (1) , Wolfgang Soergel (2) , Geordie Williamson (3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Mathematisches Institut [Freiburg]
3 MPI - Max-Planck-Institut für Mathematik

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.

Mots clés: Koszul duality; category O; formality; parity sheaves; perverse sheaves

Domaines: Théorie des représentations [math.RT]

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