The emerging p-adic Langlands programme

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Ordinary representations of G(Q_p) and fundamental algebraic representations (2012, background): “ 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 representation ρ: Gal(Qp/Qp”
On the p-adic cohomology of the Lubin-Tate tower (2015, methodology): “The goal of this paper is to provide further evidence for the existence of a p-adic local Langlands correspondence, as was first envisioned by Breuil, [2], and established for GL2(Qp) by Colmez, [12], Paskunas, [25], and others.”
General Serre weight conjectures (2015, background): “ations of the conjecture to other groups and number ﬁelds. This is now known to be true for GL2 over Q ([Col10, Eme10]) and the set W(¯r) intervenes naturally from this point of view (see for example [Bre10]). There is considerable evidence that such a philosophy remains true in more general setting”