Cohomologie p-adique de la tour de Drinfeld: le cas de la dimension 1

TL;DR

This paper computes the p-adic étale cohomology of Drinfeld's half-plane coverings and demonstrates its connection to the p-adic local Langlands correspondence for 2-dimensional de Rham representations.

Contribution

It establishes a link between p-adic geometric cohomology of Drinfeld's tower and the p-adic local Langlands correspondence for specific 2D de Rham representations.

Findings

Cohomology encodes p-adic local Langlands correspondence

Results apply to base field Q_p

Focus on 2-dimensional de Rham representations of weights 0 and 1

Abstract

We compute the p-adic geometric \'etale cohomology of the coverings of Drinfeld's half-plane, and we show that, if the base field is Q_p, this cohomology encodes the p-adic local Langlands correspondence for 2-dimensional de Rham representations (of weight 0 and 1).