The Breuil--Mezard conjecture for quaternion algebras

الأصل · EN

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.