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The Breuil-Mézard conjecture for quaternion algebras. (La conjecture de Breuil-Mézard pour les algèbres de quaternions.) (English. French summary) Zbl 1395.11085
Summary: We formulate a version of the Breuil-Mézard conjecture for quaternion algebras, and show that it follows from the Breuil-Mézard conjecture for $$\mathrm{GL}_2$$. In the course of the proof we establish a mod $$p$$ analogue of the Jacquet-Langlands correspondence for representations of $$\mathrm{GL}_2(k)$$, $$k$$ a finite field of characteristic $$p$$.

##### MSC:
 11F80 Galois representations 11F33 Congruences for modular and $$p$$-adic modular forms
##### Keywords:
Galois representations; Breuil-Mézard conjecture
Full Text:
##### References:
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