Towards a Modulo p Langlands Correspondence for GL2

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Lattices in the cohomology of Shimura curves (2013, methodology): “2 of [9] or Proposition 1.”
The p-adic local Langlands correspondence for GL_2(Q_p) (2013, background): “The proof of the claim is a variation of the construction, which first appeared in [47], and then was generalized in [12] and [36].”
On the p-adic cohomology of the Lubin-Tate tower (2015, background): “So far, little is known beyond GL2(Qp), and work of Breuil-Paskunas, [3], shows that already for GL2(F ), F 6= Qp, the situation is very difficult.”