Irreducible modular representations of the Borel subgroup of GL₂(Q_p)

2012/02/16 by Laurent Berger, Berger, Laurent, Mathieu Vienney +1
Mathematics · #11F #11S #20C #20G #22E #46A #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F #msc:11S #msc:20C #msc:20G #msc:22E #msc:46A

paper · pdf · doi:10.48550/arxiv.1202.3609

Second version : some minor corrections; some proofs have been added

arxiv created 2012/03/21 · arxiv updated 2012/03/22

Abstract

Let E be a finite extension of Fp. Using Fontaine's theory of (phi,Gamma)-modules, Colmez has shown how to attach to any irreducible E-linear representation of Gal(Qpbar/Qp) an infinite dimensional smooth irreducible E-linear representation of B₂(Qp) that has a central character. We prove that every such representation of B₂(Qp) arises in this way. Our proof extends to algebraically closed fields E of characteristic p. In this case, infinite dimensional smooth irreducible E-linear representations of B₂(Qp) having a central character arise in a similar way from irreducible E-linear representations of the Weil group of Qp.

Related

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