The Breuil–Mézard Conjecture for quaternion algebras
Annales de l'Institut Fourier, Volume 65 (2015) no. 4, p. 1557-1575
We formulate a version of the Breuil–Mézard conjecture for quaternion algebras, and show that it follows from the Breuil–Mézard conjecture for GL 2 . In the course of the proof we establish a mod p analogue of the Jacquet–Langlands correspondence for representations of GL 2 (k), k a finite field of characteristic p.
Nous formulons une version de la conjecture de Breuil–Mézard pour les algèbres de quaternions. Nous montrons que cette version est une consequence de la version originale pour GL 2 . Une partie de la démonstration est la construction d’un analogue modulo p de la correspondance de Jacquet–Langlands pour les représentations de GL 2 (k) ou k est un corps fini de caractéristique p.
Received : 2013-12-03
Accepted : 2015-03-06
Published online : 2015-11-09
Classification:  11F80,  11F33
Keywords: Galois representations, Breuil–Mézard Conjecture
@article{AIF_2015__65_4_1557_0,
     author = {Gee, Toby and Geraghty, David},
     title = {The Breuil--M\'ezard Conjecture for quaternion algebras},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {4},
     year = {2015},
     pages = {1557-1575},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2015__65_4_1557_0}
}
Gee, Toby; Geraghty, David. The Breuil–Mézard Conjecture for quaternion algebras. Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1557-1575. https://aif.centre-mersenne.org/item/AIF_2015__65_4_1557_0/

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