The Breuil-Mezard conjecture for non-scalar split residual representations

Yongquan Hu (1) , Fucheng Tan (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics [Lansing]

We prove the Breuil-Mezard conjecture for split non-scalar residual representations of Gal(Qp/Qp) by local methods. Combined with the cases previously proved in [18] and [24], this completes the proof of the conjecture (when p>3). As a consequence, the local restriction in the proof of the Fontaine-Mazur conjecture in [18] is removed.

Mots clés: Galois representations; p-adic local Langlands correspondence; Breuil-Mézard conjecture

Domaines: Théorie des nombres [math.NT]

Yongquan Hu, Fucheng Tan. The Breuil-Mezard conjecture for non-scalar split residual representations. Annales Scientifiques de l'École Normale Supérieure, 2015, 48 (6), pp.1383-1421. ⟨hal-00906113⟩