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SUMMARY:Stefano Morra (Paris 13)
DTSTART:20210610T160000Z
DTEND:20210610T172000Z
DTSTAMP:20260423T021300Z
UID:RAMpAGe/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/46/"
 >Moduli of Fontaine–Laffaille modules and local–global compatibility m
 od p</a>\nby Stefano Morra (Paris 13) as part of Recent Advances in Modern
  p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nThe mod $p$-local Langlands prog
 ram generated from the observation that certain invariants\non local Galoi
 s deformation rings can be predicted by the mod $p$ representation theory 
 of $p$-adic $\\mathbf{GL}_n$. A first attempt to give evidence for this pr
 ogram is in the expected local–global compatibility\, namely that the co
 rrespondence will be realized in Hecke eigenspaces of the cohomology of lo
 cally symmetric spaces with infinite level at p. In this talk we prove one
  direction of this expectation\, namely that the smooth $\\mathbf{GL}_n(\\
 mathbb{Q}_{p^f})$ action on Hecke eigenspaces\nin the mod $p$ cohomology o
 f compact unitary groups with infinite level at $p$ determines the\nlocal 
 Galois parameter at $p$-adic places\, when the latter parameters are Fonta
 ine–Laffaille.\nThis is joint work in progress with D. Le\, B. Le Hung\,
  C. Park and Z. Qian.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/46/
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