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

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.

33 pages

References in corpus (1)

• Coefficient systems and supersingular representations of $G{L}_2(F)$

Cited by in corpus (5)

• The universal family of semi-stable p-adic Galois representations
• Infinitesimal characters in arithmetic families
• On crystabelline deformation rings of $\mathrm{Gal}({\overline{\mathbb{Q}}}_p/{\mathbb{Q}}_p)$ (with an appendix by Jack Shotton)
• Sur un problème de compatibilité local-global localement analytique
• On a relation of overconvergence and $F$-analyticity on $p$-adic Galois representations of a $p$-adic field $F$