Co-t-structures on coherent sheaves and the Humphreys conjecture

Abstract: Let G be a connected reductive group over an algebraically closed field, and let C be a nilpotent orbit for G. If L is an irreducible G-equivariant vector bundle on C, then one can define a "coherent intersection cohomology complex" IC(C,L). These objects play an important role in various results related to the local geometric Langlands program.

When G has positive characteristic, instead of an irreducible bundle L, one might consider a tilting bundle T on C. I will explain a new construction that associates to the pair (C,T) a complex of coherent sheaves S(C,T) with remarkable Ext-vanishing properties. This construction leads to a proof of a conjecture of Humphreys on (relative) support varieties for tilting modules, and hints at a kind of "recursive" structure in the tensor category of tilting G-modules. This work is joint with W. Hardesty (and also partly with S. Riche).

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.