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Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture

MPS-Authors
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Mautner,  Carl
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

https://doi.org/10.4171/JEMS/812
(Publisher version)

Fulltext (public)

1501.07369.pdf
(Preprint), 675KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Mautner, C., & Riche, S. (2018). Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture. Journal of the European Mathematical Society, 20(9), 2259-2332. doi:10.4171/JEMS/812.


Cite as: http://hdl.handle.net/21.11116/0000-0005-6F17-6
Abstract
Let $\mathbf{G}$ be a connected reductive group over an algebraically closed field $\mathbb{F}$ of good characteristic, satisfying some mild conditions. In this paper we relate tilting objects in the heart of Bezrukavnikov's exotic t-structure on the derived category of equivariant coherent sheaves on the Springer resolution of $\mathbf{G}$, and Iwahori-constructible $\mathbb{F}$-parity sheaves on the affine Grassmannian of the Langlands dual group. As applications we deduce in particular the missing piece for the proof of the Mirkovic-Vilonen conjecture in full generality (i.e. for good characteristic), a modular version of an equivalence of categories due to Arkhipov-Bezrukavnikov-Ginzburg, and an extension of this equivalence.