Revêtements du demi-plan de Drinfeld et correspondance de Langlands p-adique
arXiv:1509.00606
Abstract
We describe the de Rham complex of the étale coverings of Drinfeld's p-adic upper half-plane for GL_2(Q_p). Conjectured by Breuil and Strauch, this description gives a geometric realization of the p-adic local Langlands correspondence for certain two-dimensional de Rham representations of the absolute Galois group of Q_p.
Final version, to appear in the Annals of Math