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On the exotic t-structure in positive characteristic. (English) Zbl 1404.14022

Summary: In this paper, we study Bezrukavnikov’s exotic t-structure on the derived category of equivariant coherent sheaves on the Springer resolution of a connected reductive algebraic group defined over a field of positive characteristic with simply connected derived subgroup. In particular, we show that the heart of the exotic t-structure is a graded highest weight category, and we study the tilting objects in this heart. Our main tool is the “geometric braid group action” studied by Bezrukavnikov and the second author.

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14L10 Group varieties
14M15 Grassmannians, Schubert varieties, flag manifolds