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A Langlands dual realization of coherent sheaves on the nilpotent cone
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abstract
Let $G$ and $\check{G}$ be Langlands dual connected reductive groups. We establish a monoidal equivalence of $\infty$-categories between equivariant quasicoherent sheaves on the formal neighborhood of the nilpotent cone in $G$ and Steinberg-Whittaker D-modules on the loop group of $\check{G}$, as conjectured by Bezrukavnikov. More generally, we establish equivalences between various spectral and automorphic realizations of affine Hecke categories and their modules, confirming conjectures of Bezrukavnikov.
Forward citations
Cited by 3 Pith papers
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Endoscopy for metaplectic affine Hecke categories
Monodromic affine Hecke categories for centrally extended loop groups are equivalent to Soergel bimodule categories, yielding endoscopic equivalences and the metaplectic derived Satake equivalence.
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Tame local Betti geometric Langlands
The authors prove the tame local Betti geometric Langlands correspondence, a monoidal equivalence between ind-coherent sheaves on a Steinberg stack and nilpotent-singular-support Betti sheaves on a monodromic Hecke stack.
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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.
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