Extensions de représentations de de Rham et vecteurs localement algébriques

Abstract

Let $\Pi$ be an irreducible unitary completion of a locally algebraic ${\rm GL}_2(\qp)$-representation. We describe those first-order deformations of $\Pi$ which are themselves completions of a locally algebraic representation. This answers a question of Paskunas and has direct applications to the Breuil-Mézard conjecture.

in French

References in corpus (3)

• On the Breuil-Mézard conjecture
• Complétés universels de représentations de GL_2(Q_p)
• The p-adic local Langlands correspondence for GL_2(Q_p)

Cited by in corpus (6)

• On 2-dimensional 2-adic Galois representations of local and global fields
• The p-adic local Langlands correspondence for GL_2(Q_p)
• The Breuil-Mezard conjecture for non-scalar split residual representations
• Revêtements du demi-plan de Drinfeld et correspondance de Langlands p-adique
• Higher $\mathcal{L}$-invariants for ${\mathrm{GL}}_3({\mathbb{Q}}_p)$ and local-global compatibility
• Sur un problème de compatibilité local-global localement analytique