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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
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