an:06541661
Zbl 1395.11085
Gee, Toby; Geraghty, David
The Breuil-M??zard conjecture for quaternion algebras
EN
Ann. Inst. Fourier 65, No. 4, 1557-1575 (2015).
00352546
2015
j
11F80 11F33
Galois representations; Breuil-M??zard conjecture
Summary: We formulate a version of the Breuil-M??zard conjecture for quaternion algebras, and show that it follows from the Breuil-M??zard 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 \(p\).