Breuil--Mézard conjectures for central division algebras

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• Andrea Dotto (Imperial College)
• Tuesday 07 May 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

The Breuil—Mézard conjecture relates the special fibers of local Galois deformation rings to the mod p reduction of types for GL(n). The known cases of this relation have powerful global consequences, and provide evidence for the existence of a p-adic local Langlands correspondence.

In this talk we show that the conjecture implies an analogous statement for discrete series Galois deformations and unit groups of p-adic central division algebras. The main step is to construct a Jacquet—Langlands transfer of Serre weights to GL(n), and to prove its compatibility with the reduction of types: this requires to prove a conjecture of Broussous, Sécherre and Stevens on the explicit description of the Jacquet—Langlands correspondence.

This talk is part of the Number Theory Seminar series.

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