Abstract
Nous décrivons le complexe de de Rham des revêtements du demi-plan de Drinfeld pour ${\rm GL}_2(\mathbf{Q}_p)$. Cette description, conjecturée par Breuil et Strauch, fournit une réalisation géométrique de la correspondance de Langlands locale $p$-adique pour certaines représentations de de Rham de dimension $2$ de ${\rm Gal}(\overline{\mathbf{Q}_p}/\mathbf{Q}_p)$.
We describe the de Rham complex of the étale coverings of Drinfeld’s $p$-adic upper half-plane for ${\rm GL}_2(\mathbf{Q}_p)$. 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 ${\rm Gal}(\overline{\mathbf{Q}_p}/\mathbf{Q}_p)$.
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}