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SUMMARY:Richard Magner (Boston University)
DTSTART:20200813T160000Z
DTEND:20200813T172000Z
DTSTAMP:20260423T052622Z
UID:RAMpAGe/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/9/">
 On the Cohomology of Moduli of Mixed Characteristic Shtukas</a>\nby Richar
 d Magner (Boston University) as part of Recent Advances in Modern p-Adic G
 eometry (RAMpAGe)\n\n\nAbstract\nWe review mixed characteristic shtukas an
 d their moduli. These generalize the Lubin-Tate tower and other Rapoport-Z
 ink spaces.  Under the Kottwitz conjecture\, the cohomology of these space
 s are expected to realize the local Langlands correspondence.  The data de
 fining these spaces involve cocharacters of a Lie group\;  when the cochar
 acter is minuscule\, we recover classical Rapoport-Zink spaces.  In the ca
 se of $\\mathrm{GL}_n$\, we show that the Kottwitz conjecture for general 
 cocharacters can be reduced to the minuscule case.  This depends on a geom
 etric Satake equivalence for the $B_{\\mathrm{dR}}$-affine Grassmanian\, d
 ue to Fargues and Scholze\, and a formula of Imai on cohomology derived fr
 om it.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/9/
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