Représentations potentiellement triangulines de dimension 2

Laurent Berger (1) , Gaëtan Chenevier (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 CMLS - Centre de Mathématiques Laurent Schwartz

The two main results of this note are on the one hand that if V is a 2-dimensional potentially trianguline representation of G_Qp then V satisfies at least one of the following properties (1) V is split trianguline (2) V is a direct sum of characters or an induced representation (3) V is a twist of a de Rham representation, and on the other hand that there exists some 2-dimensional representations of G_Qp which are not potentially trianguline.

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

Laurent Berger, Gaëtan Chenevier. Représentations potentiellement triangulines de dimension 2. Journal de Théorie des Nombres de Bordeaux, 2010, 22 (3), pp.557--574. ⟨hal-00605399⟩