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SUMMARY:Jared Weinstein (Boston University)
DTSTART:20211012T160000Z
DTEND:20211012T172000Z
DTSTAMP:20260423T021306Z
UID:RAMpAGe/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/52/"
 >Bun_G minicourse:  Lefschetz formula for diamonds</a>\nby Jared Weinstein
  (Boston University) as part of Recent Advances in Modern p-Adic Geometry 
 (RAMpAGe)\n\n\nAbstract\nThis talk is the third part of a six-part series 
 "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\, held Tue
 sdays and Thursdays between 5 and 21 October\, 2021.\n\nSeries abstract:  
 The recent manuscript of Fargues-Scholze aims to "geometrize" the Langland
 s program for a p-adic group $G$\, by relating the players in that story t
 o the stack $\\mathrm{Bun}_G$.  Following a strategy of V. Lafforgue\, the
  main result of [FS] is the construction of an L-parameter attached to a s
 mooth irreducible representation of $G$.\n\nThe goal of this series is to 
 review the main ideas of this work\, and to discuss two related results:  
 progress on the Kottwitz conjecture for local shtuka spaces by Hansen-Kale
 tha-Weinstein\,  and the construction of eigensheaves on $\\mathrm{Bun}_G$
  when $G=\\mathrm{GL}_n$ by Anschütz-le Bras. \n\nTalk abstract:  In this
  talk we will discuss a very general form of the Lefschetz-Verdier trace f
 ormula which applies to stacks (both of schemes and of diamonds).  As an a
 pplication\, we will show that if a locally pro-$p$ group $G$ acts on a pr
 oper diamond $X$\, and if $A$ is a $G$-equivariant $\\ell$-adic sheaf on $
 X$ which is "dualizable" (= universally locally acyclic)\, then the cohomo
 logy $R\\Gamma(X\,A)$ is an admissible representation of $G$\, whose Haris
 h-Chandra distribution can be computed in terms of local terms living on t
 he fixed-point locus of $G$ on $X$.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/52/
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