Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture

Pramod N. Achar Department of Mathematics, Louisiana State University Laura Rider Department of Mathematics, Massachusetts Institute of Technology

Representation Theory mathscidoc:1701.30002

Acta Mathematica, 215, (2), 183-216, 2014.7
We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no$p$-torsion, as long as$p$is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when$p$is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau–Mautner–Williamson theory of parity sheaves.
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@inproceedings{pramod2014parity,
  title={Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture},
  author={Pramod N. Achar, and Laura Rider},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405670040808},
  booktitle={Acta Mathematica},
  volume={215},
  number={2},
  pages={183-216},
  year={2014},
}
Pramod N. Achar, and Laura Rider. Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture. 2014. Vol. 215. In Acta Mathematica. pp.183-216. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405670040808.
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