The p-adic local Langlands correspondence for GL_2(Q_p)

By Pierre Colmez, G. Dospinescu, Vytautas Paškūnas. 2013

61 citations recorded by the source corpus.

The p-adic local Langlands correspondence for GL_2(Q_p) is given by an exact functor from unitary Banach representations of GL_2(Q_p) to representations of the absolute Galois group G_{Q_p} of Q_p. We prove, using characteristic 0 methods, that this correspondence induces a bijection between absolutely irreducible non-ordinary representations of GL_2(Q_p) and absolutely irreducible 2-dimensional representations of G_{Q_p}. This had already been proved, by characteristic p methods, but only for p\geq 5.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0e6a267919eb5fc512db58632aefe1c08f75ae5e

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In Geometry and Topology

1. C. Breuil
2. F. Herzig
3. T. Gee
4. Vytautas Paškūnas
5. Peter Scholze
6. M. Emerton
7. M. Kisin
8. B. Bhatt

In Mathematical Physics

1. C. Breuil
2. F. Herzig
3. T. Gee
4. Vytautas Paškūnas
5. Peter Scholze
6. M. Emerton
7. M. Kisin
8. B. Bhatt

Citations in the corpus

• Ordinary representations of G(Q_p) and fundamental algebraic representations (2012, background): “n unitary continuous representations II 72 1 Introduction The p-adic Langlands programme for the group GL2(Qp) is now well understood, both from a local and a global point of view ([Col10], [Paˇs13], [CDP], [Eme11], see [Bre10] for an overview). In particular, to (essentially) any continuous represe”