Invariant elements for p-modular representations of GL2(Qp)

Stefano Morra (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Let p be an odd rational prime and F a p-adic field. We give a realization of the universal p- modular representationsof GL2(F) in terms of an explicit Iwasawa module. We specialize our constructions to the case F = Qp , giving a detailed description of the invariants under principal congruence subgroups of irreducible admissible p-modular representations of GL2(Qp), generalizing previous works of Breuil and Paskunas. We apply these results to the local/global compatibility of Emerton, giving a generalization of the classical multiplicity one results for the Jacobians of modularcurves with arbitrary level at p.

Mots clés: Supersingular representation; P-adic Langlands correspondence; Supersingular representation.

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

Stefano Morra. Invariant elements for p-modular representations of GL2(Qp). 2013. ⟨hal-00576945v3⟩