Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture - Archive ouverte HAL Access content directly
Journal Articles Journal of the European Mathematical Society Year : 2018

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

Abstract

Let G be a connected reductive group over an algebraically closed field 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 G, and Iwahori-constructible 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.
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Dates and versions

hal-01110852 , version 1 (29-01-2015)
hal-01110852 , version 2 (18-06-2015)
hal-01110852 , version 3 (30-06-2016)

Identifiers

  • HAL Id : hal-01110852 , version 3

Cite

Carl Mautner, Simon Riche. Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture. Journal of the European Mathematical Society, 2018, 20, pp.2259-2332. ⟨hal-01110852v3⟩
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