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SUMMARY:Christian Klevdal (University of Utah)
DTSTART:20211014T223000Z
DTEND:20211014T233000Z
DTSTAMP:20260422T055509Z
UID:SFUQNTAG/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/52/
 ">Integrality of $G$-local systems</a>\nby Christian Klevdal (University o
 f Utah) as part of SFU NT-AG seminar\n\n\nAbstract\nSimpson conjectured th
 at for a reductive group $G$\, rigid $G$-local systems on a smooth project
 ive complex variety are integral. I will discuss a proof of integrality fo
 r cohomologically rigid $G$-local systems. This generalizes and is inspire
 d by work of Esnault and Groechenig for $GL_n$. Surprisingly\, the main to
 ols used in the proof (for general $G$ and $GL_n$) are the work of L. Laff
 orgue on the Langlands program for curves over function fields\, and work 
 of Drinfeld on companions of $\\ell$-adic sheaves. The major differences b
 etween general $G$ and $GL_n$ are first to make sense of companions for $G
 $-local systems\, and second to show that the monodromy group of a rigid G
 -local system is semisimple. All work is joint with Stefan Patrikis.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/52/
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