The Breuil--Mezard conjecture for quaternion algebras

Abstract

We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL_2. In the course of the proof we establish a mod p analogue of the Jacquet--Langlands correspondence for representations of GL_2(k), k a finite field of characteristic p.

15 pages