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SUMMARY:Pramod Achar (LSU)
DTSTART:20220511T200000Z
DTEND:20220511T210000Z
DTSTAMP:20260423T035416Z
UID:MITLie/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/55/">
 Co-t-structures on coherent sheaves and the Humphreys conjecture</a>\nby P
 ramod Achar (LSU) as part of MIT Lie groups seminar\n\nLecture held in 2-1
 42.\n\nAbstract\nLet G be a connected reductive group over an algebraicall
 y closed field\, and let C be a nilpotent orbit for G.  If L is an irreduc
 ible G-equivariant vector bundle on C\, then one can define a "coherent in
 tersection cohomology complex" IC(C\,L). These objects play an important r
 ole in various results related to the local geometric Langlands program. \
 n\nWhen G has positive characteristic\, instead of an irreducible bundle L
 \, one might consider a tilting bundle T on C.  I will explain a new const
 ruction 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 fo
 r tilting modules\, and hints at a kind of "recursive" structure in the te
 nsor category of tilting G-modules.  This work is joint with W. Hardesty (
 and also partly with S. Riche).\n
LOCATION:https://researchseminars.org/talk/MITLie/55/
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