The affine Grassmannian and the Springer resolution in positive characteristic

Abstract

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.

50 pages; with an appendix joint with Simon Riche. v2: minor corrections

References in corpus (1)

• Modular perverse sheaves on flag varieties II: Koszul duality and formality

Cited by in corpus (1)

• Billiards and Tilting Characters for ${\mathrm{SL}}_3$