Revêtements du demi-plan de Drinfeld et correspondance de Langlands $p$-adique

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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Authors

Gabriel Dospinescu

CNRS, UMPA, École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon, France

Arthur-César Le Bras

DMA - Ecole Normale Supérieure, 45, rue d'Ulm, 75230 Paris Cedex 05, France