The universal monodromic Arkhipov-Bezrukavnikov equivalence identifies universal monodromic Iwahori-Whittaker sheaves with quasicoherent sheaves on the Grothendieck alteration, plus a monoidal bi-Whittaker equivalence.
Central sheaves on affine flag varieties
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The universal monodromic Arkhipov--Bezrukavnikov equivalence
The universal monodromic Arkhipov-Bezrukavnikov equivalence identifies universal monodromic Iwahori-Whittaker sheaves with quasicoherent sheaves on the Grothendieck alteration, plus a monoidal bi-Whittaker equivalence.