The image of Colmez's Montreal functor

Vytautas Paskunas

The image of Colmez's Montreal functor

Representation Theory 2013-01-08 v3 Number Theory

Authors: Vytautas Paskunas

Abstract

We prove a conjecture of Colmez concerning the reduction modulo $p$ of invariant lattices in irreducible admissible unitary $p$ -adic Banach space representations of $GL_2(Q_p)$ with $p\ge 5$ . This enables us to restate nicely the $p$ -adic local Langlands correspondence for $GL_2(Q_p)$ and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.

Keywords

Colmez Montreal functor p-adic local Langlands correspondence invariant lattices unitary Banach space representations reduction modulo p

Cite

@article{arxiv.1005.2008,
  title  = {The image of Colmez's Montreal functor},
  author = {Vytautas Paskunas},
  journal= {arXiv preprint arXiv:1005.2008},
  year   = {2013}
}

Comments

Proof of Prop. 5.16 modified

Related papers

View all related →