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SUMMARY:Jack Sempliner (Imperial College London)
DTSTART:20211201T150000Z
DTEND:20211201T160000Z
DTSTAMP:20260418T064344Z
UID:LNTS/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/54/">On
  the almost-product structure on the moduli of bounded global $G$-shtuka</
 a>\nby Jack Sempliner (Imperial College London) as part of London number t
 heory seminar\n\nLecture held in Huxley 144\, Imperial.\n\nAbstract\nLet $
 X$ be an algebraic curve over $\\mathbb{F}_q$ and $G$ be a reductive algeb
 raic group over $\\mathbb{F}_q(X)$. Under mild technical hypotheses we con
 struct families of stacks over the moduli $\\text{Sht}_{G\, X\, I}^{\\mu_*
 }$ of bounded global $G$-shtuka (a small generalization of the stacks stud
 ied by Lafforgue and Varshavsky) which provide natural analogues of Igusa 
 varieties in the function field setting. Our main result is an isomorphism
  between certain Igusa varieties associated to moduli of shtuka for reduct
 ive groups $G\, G'$ which are related by an inner twist. Along the way we 
 prove an almost-product formula computing the compactly supported cohomolo
 gy of the special fibers of $\\text{Sht}_{G\, X\, I}^{\\mu_*}$ with trivia
 l coefficients in terms of the cohomology of our Igusa stacks and a functi
 on-field analogue of Rapoport-Zink spaces constructed in previous work of 
 Hartl and Arasteh Rad.\n
LOCATION:https://researchseminars.org/talk/LNTS/54/
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