The p-adic local Langlands correspondence for GL₂(Qₚ)

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 Qp 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 Qp . This had already been proved, by characteristic p methods, but only for p 5.