On the exotic t-structure in positive characteristic

TL;DR

This paper investigates Bezrukavnikov's exotic t-structure on the derived category of equivariant coherent sheaves over the Springer resolution in positive characteristic, revealing its heart as a graded highest weight category and analyzing tilting objects.

Contribution

It demonstrates that the heart of the exotic t-structure forms a graded highest weight category and explores the properties of tilting objects within it, using geometric braid group actions.

Findings

The heart of the exotic t-structure is a graded highest weight category.

Tilting objects in this heart are characterized and studied.

The geometric braid group action is a key tool in the analysis.

Abstract

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.