no. 4
The Breuil–Mézard Conjecture for quaternion algebras
[La conjecture de Breuil–Mézard pour les algèbres de quaternions]
Gee, Toby1 ; Geraghty, David2
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)
Annales de l'Institut Fourier, Tome 65 (2015) no. 4, pp. 1557-1575.

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.

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.

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, Tome 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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