# Irreducible modular representations of the Borel subgroup of GL_2(Q_p)

Abstract : Let E be a finite extension of Fp. Using Fontaine's (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 B_2(Qp) that has a central character. We prove that every such representation of B_2(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 B_2(Qp) having a central character arise in a similar way from irreducible E-linear representations of the Weil group of Qp.
Document type :
Book sections
Domain :

https://hal.archives-ouvertes.fr/hal-00671261
Contributor : Laurent Berger <>
Submitted on : Friday, February 17, 2012 - 9:15:58 AM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM

### Identifiers

• HAL Id : hal-00671261, version 1
• ARXIV : 1202.3609

### Citation

Laurent Berger, Mathieu Vienney. Irreducible modular representations of the Borel subgroup of GL_2(Q_p). Cambridge Univ. Press. Automorphic Forms and Galois Representations, 414, 2014, London Math. Soc. Lecture Note Ser. ⟨hal-00671261⟩

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