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SUMMARY:Siyan Daniel Li-Huerta (Harvard)
DTSTART:20220323T160000Z
DTEND:20220323T172000Z
DTSTAMP:20260423T021300Z
UID:RAMpAGe/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/67/"
 >The plectic conjecture over local fields</a>\nby Siyan Daniel Li-Huerta (
 Harvard) as part of Recent Advances in Modern p-Adic Geometry (RAMpAGe)\n\
 n\nAbstract\nThe étale cohomology of varieties over $\\mathbf{Q}$ enjoys 
 a Galois action. In the case of Hilbert modular varieties\, Nekovář-Scho
 ll observed that this Galois action on the level of cohomology extends to 
 a much larger profinite group: the plectic group. They conjectured that th
 is extension holds even on the level of complexes\, as well as for more ge
 neral Shimura varieties.\n\nWe present a proof of the analogue of this con
 jecture for local Shimura varieties. This implies that\, for p-adically un
 iformized global Shimura varieties\, we obtain an action of the local plec
 tic group on the level of complexes. The proof crucially uses Fargues–Sc
 holze's results on the cohomology of moduli spaces of local shtukas.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/67/
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