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SUMMARY:Christian Klevdal (University of Utah)
DTSTART:20210429T210000Z
DTEND:20210429T220000Z
DTSTAMP:20260423T005847Z
UID:UCSD_NTS/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/35/
 ">Integrality of G-local systems</a>\nby Christian Klevdal (University of 
 Utah) as part of UCSD number theory seminar\n\nLecture held in normally AP
 M 7321\, currently online.\n\nAbstract\nSimpson conjectured that for a red
 uctive group $G$\, rigid $G$-local systems on a smooth projective complex 
 variety are integral. I will discuss a proof of integrality for cohomologi
 cally rigid $G$-local systems. This generalizes and is inspired by work of
  Esnault and Groechenig for $GL_n$. Surprisingly\, the main tools used in 
 the proof (for general $G$ and $GL_n$) are the work of L. Lafforgue on the
  Langlands program for curves over function fields\, and work of Drinfeld 
 on companions of $\\ell$-adic sheaves. The major differences between gener
 al $G$ and $GL_n$ are first to make sense of companions for $G$-local syst
 ems\, and second to show that the monodromy group of a rigid G-local syste
 m is semisimple. All work is joint with Stefan Patrikis.\n\npre-talk\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/35/
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