Représentations cristallines irréductibles de \rm GL₂(Q_p)

2004/10/04 by Laurent Berger, Christophe Breuil, Berger, Laurent +1
Mathematics · #11F #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F

paper · pdf · doi:10.48550/arxiv.math/0410053

44 pages, in french

arxiv created 2004/10/04 · arxiv updated 2009/12/01

Abstract

In \cite[\S1.3]Br2, some unitary representations of \rm GL₂(Q_p) on p-adic Banach spaces are associated to 2-dimensional irreducible crystalline representations of \rm Gal(Q_p)/Q_p). Some conjectures are formulated concerning those Banach spaces (non triviality, topological irreducibility, admissibility). We prove those conjectures by reinterpreting those Banach as spaces of functions of a certain type on Q_p, and then by using the theory of (ϕ,Γ)-modules associated to the corresponding crystalline representations.

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