The Breuil–Mézard Conjecture for quaternion algebras
[La conjecture de Breuil–Mézard pour les algèbres de quaternions]
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.

Reçu le :
Accepté le :
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DOI : https://doi.org/10.5802/aif.2967
Classification : 11F80,  11F33
Mots clés : Représentations galoisiennes, Conjecture de Breuil–Mézard
@article{AIF_2015__65_4_1557_0,
     author = {Gee, Toby and Geraghty, David},
     title = {The {Breuil{\textendash}M\'ezard} {Conjecture} for quaternion algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {1557--1575},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {65},
     number = {4},
     year = {2015},
     doi = {10.5802/aif.2967},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2967/}
}
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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