Speaker: Pramod Achar (LSU)

Title: 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).