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SUMMARY:Breuil--Mézard conjectures for central division algebras - Andrea
  Dotto (Imperial College)
DTSTART:20190507T133000Z
DTEND:20190507T143000Z
UID:TALK123667@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:The Breuil--Mézard conjecture relates the special fibers of l
 ocal Galois deformation rings to the mod p reduction of types for GL(n). T
 he known cases of this relation have powerful global consequences\, and pr
 ovide evidence for the existence of a p-adic local Langlands correspondenc
 e.\n\nIn this talk we show that the conjecture implies an analogous statem
 ent for discrete series Galois deformations and unit groups of p-adic cent
 ral division algebras. The main step is to construct a Jacquet--Langlands 
 transfer of Serre weights to GL(n)\, and to prove its compatibility with t
 he reduction of types: this requires to prove a conjecture of Broussous\, 
 Sécherre and Stevens on the explicit description of the Jacquet--Langland
 s correspondence.
LOCATION:MR13
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