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Modular Koszul duality

  • Simon Riche (a1) (a2), Wolfgang Soergel (a3) and Geordie Williamson (a4)
Abstract

We prove an analogue of Koszul duality for category $ \mathcal{O} $ of a reductive group $G$ in positive characteristic $\ell $ 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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References
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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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