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

Abstract

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.

Final version. To appear in Ann. Scient. de l'E.N.S

References in corpus (2)

• On the Breuil-Mézard conjecture
• Extensions de représentations de de Rham et vecteurs localement algébriques

Cited by in corpus (3)

• On the Breuil-Mézard conjecture
• A local proof of the Breuil-Mézard conjecture in the scalar semi-simplification case
• A simplified proof of Serre's Conjectures