The Breuil--Mezard conjecture for quaternion algebras

2013/08/30 by Gee, Toby, Geraghty, David · 1 citation
#11F33 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1309.0019

Abstract

We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL₂. In the course of the proof we establish a mod p analogue of the Jacquet--Langlands correspondence for representations of GL₂(k), k a finite field of characteristic p.

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• On the finite length of some p-adic representations of the quaternion algebra over \Q_p

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