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SUMMARY:Multivariable (φ\, Γ)-modules and local global compatibility for
  the mod p cohomology of Shimura curves - Stefano Morra (Université de Pa
 ris Saint-Denis)
DTSTART:20230509T133000Z
DTEND:20230509T143000Z
UID:TALK200359@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Let K be a finite unramified extension of Qp. Using techniques
  from perfectoid geometry\nwe describe functors from the category of conti
 nuous finite dimensional mod p representations\nof Gal(Qp/K)\, and from th
 e category of smooth mod p representations of GL2(K)\, into a\ncategory of
  multivariable (φ\, O\n×\nK)-modules. We state a conjecture towards the 
 mod p local\nLanglands program relating the two functors\, and prove it in
  several cases: if K is the completion at a p-adic place of a totally real
  field F\, r : Gal(Q/F) → GL2(Fp) a modular Galois\nrepresentation which
  is tame and sufficiently generic at Gal(Qp/K)\, and π is the smooth repr
 esentation cut out by the r-eigenspace in the cohomology of a Shimura curv
 e with infinite\nlevel at p\, then the two functors produce the same (φ\,
  O\n×\nK)-module.\nThis is a report on a series of work joint with C. Bre
 uil\, F. Herzig\, Y. Hu et B. Schraen.
LOCATION:MR15
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