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SUMMARY:Chenji Fu (Bonn University)
DTSTART:20230913T060000Z
DTEND:20230913T070000Z
DTSTAMP:20260423T005843Z
UID:PekiNT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PekiNT/12/">
 Explicit categorical mod l local Langlands correspondence for depth-zero s
 upercuspidal part of GL_2</a>\nby Chenji Fu (Bonn University) as part of P
 KU/BICMR Number Theory Seminar\n\nLecture held in Room 77201\, BICMR.\n\nA
 bstract\nLet $F$ be a non-archimedean local field. I will explicitly descr
 ibe:\n\n(1) (The category of quasicoherent sheaves on) The connected compo
 nent of the moduli space of Langlands parameters over $\\overline{\\mathbb
 {Z}_l}$ containing an irreducible tame L-parameter with $\\overline{\\math
 bb{F}_l}$ coefficients\;\n(2) the block of the category of smooth represen
 tations of $G(F)$ with $\\overline{\\mathbb{Z}_l}$ coefficients containing
  a depth-zero supercuspidal representation with $\\overline{\\mathbb{F}_l}
 $ coefficients.\n\nThe argument works at least for (simply connected) spli
 t reductive group $G$\, but I will focus on the example of $\\mathrm{GL}_2
 $ for simplicity. The two sides turn out to match abstractly. If time perm
 its\, I will explain how to get the categorical local Langlands correspond
 ence for depth-zero supercuspidal part of $\\mathrm{GL}_2$ with $\\overlin
 e{\\mathbb{Z}_l}$ coefficients in Fargues-Scholze's form.\n\nHybrid talk\n
 \nZoom livestream: ID 743 736 2326 / Password 013049\n
LOCATION:https://researchseminars.org/talk/PekiNT/12/
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