On some modular representations of the Borel subgroup of GL_2(Q_p)

Laurent Berger (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Colmez has given a recipe to associate a smooth modular representation Omega(W) of the Borel subgroup of GL_2(Q_p) to a F_p^bar-representation W of Gal(Qp^bar/Qp) by using Fontaine's theory of (phi,Gamma)-modules. We compute Omega(W) explicitly and we prove that if W is irreducible and dim(W)=2, then Omega(W) is the restriction to the Borel subgroup of GL_2(Q_p) of the supersingular representation associated to W in Breuil's correspondence.

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Laurent Berger. On some modular representations of the Borel subgroup of GL_2(Q_p). Compositio Mathematica, 2010, 146 (1), pp.58-80. ⟨10.1112/S0010437X09004345⟩. ⟨hal-00605396⟩