Geodesic
Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković–Vilonen conjecture
Journal of the European Mathematical Society, Tome 20 (2018) no. 9, pp. 2259-2332 Cet article a éte moissonné depuis la source EMS Press

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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 Mirković–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.
DOI : 10.4171/jems/812
Classification : 22-XX, 14-XX
Keywords: Affine Grassmannian, Springer resolution, exotic t-structure, parity sheaves, Mirković–Vilonen conjecture 
@article{JEMS_2018_20_9_a6,
     author = {Carl Mautner and Simon Riche},
     title = {Exotic tilting sheaves, parity sheaves on affine {Grassmannians,} and the {Mirkovi\'c{\textendash}Vilonen} conjecture},
     journal = {Journal of the European Mathematical Society},
     pages = {2259--2332},
     year = {2018},
     volume = {20},
     number = {9},
     doi = {10.4171/jems/812},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/812/}
}
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Carl Mautner; Simon Riche. Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković–Vilonen conjecture. Journal of the European Mathematical Society, Tome 20 (2018) no. 9, pp. 2259-2332. doi: 10.4171/jems/812

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