The Breuil–Mézard Conjecture for quaternion algebras
Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 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.

DOI: 10.5802/aif.2967
Classification: 11F80, 11F33
Keywords: Galois representations, Breuil–Mézard Conjecture
Mot clés : Représentations galoisiennes, Conjecture de Breuil–Mézard
Gee, Toby 1; Geraghty, David 2

1 Department of Mathematics Imperial College London 180 Queen’s Gate London SW7 2RH (UK)
2 Department of Mathematics Boston College Carney Hall 301 Chestnut Hill MA 02467 (USA)
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Gee, Toby; Geraghty, David. The Breuil–Mézard Conjecture for quaternion algebras. Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1557-1575. doi : 10.5802/aif.2967. https://aif.centre-mersenne.org/articles/10.5802/aif.2967/

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