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.
Publication Source (Journal or Book title)
Achar, P., & Rider, L. (2016). The affine Grassmannian and the Springer resolution in positive characteristic. Compositio Mathematica, 152 (12), 2627-2677. https://doi.org/10.1112/S0010437X16007661