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 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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