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arXiv · 1310.2235

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

Pierre Colmez·Gabriel Dospinescu·Vytautas Paskunas
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Abstract

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.

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Pierre Colmez, Gabriel Dospinescu, Vytautas Paskunas. 2013-10-08. The p-adic local Langlands correspondence for GL_2(Q_p). https://arxiv.org/abs/1310.2235

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