The Breuil–Mézard Conjecture for quaternion algebras

[La conjecture de Breuil–Mézard pour les algèbres de quaternions]

Gee, Toby ; Geraghty, David

Annales de l'Institut Fourier, Tome 65 (2015), p. 1557-1575 / Harvested from Numdam

Résumé

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 $\operatorname{GL}_2$. Une partie de la démonstration est la construction d’un analogue modulo $p$ de la correspondance de Jacquet–Langlands pour les représentations de $\operatorname{GL}_2(k)$ ou $k$ est un corps fini de caractéristique $p$.

Abstract

We formulate a version of the Breuil–Mézard conjecture for quaternion algebras, and show that it follows from the Breuil–Mézard conjecture for $\operatorname{GL}_2$. In the course of the proof we establish a mod $p$ analogue of the Jacquet–Langlands correspondence for representations of $\operatorname{GL}_2(k)$, $k$ a finite field of characteristic $p$.

Détail

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/aif.2967
Classification:  11F80,  11F33
Mots clés: Représentations galoisiennes, Conjecture de Breuil–Mézard

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