Compositio Mathematica: Volume 152 -

The affine Grassmannian and the Springer resolution in positive characteristic
Part of:
- Lie groups
- (Co)homology theory
Pramod N. Achar, Laura Rider
Published online by Cambridge University Press:

28 November 2016, pp. 2627-2677
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An important result of Arkhipov–Bezrukavnikov–Ginzburg relates constructible sheaves on the affine Grassmannian to coherent sheaves on the dual Springer resolution. In this paper, we prove a positive-characteristic analogue of this statement, using the framework of ‘mixed modular sheaves’ recently developed by the first author and Riche. As an application, we deduce a relationship between parity sheaves on the affine Grassmannian and Bezrukavnikov’s ‘exotic t-structure’ on the Springer resolution.

Compositio Mathematica