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

Colmez, Pierre; Dospinescu, Gabriel; Nizioł, Wiesława

doi:10.1090/jams/935

Cohomologie $p$-adique de la tour de Drinfeld$\colon$ le cas de la dimension $1$
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by Pierre Colmez, Gabriel Dospinescu and Wiesława Nizioł

J. Amer. Math. Soc. 33 (2020), 311-362

DOI: https://doi.org/10.1090/jams/935

Published electronically: December 24, 2019

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Abstract:

We compute the $p$-adic geometric étale cohomology of the coverings of the Drinfeld half-plane, and we show that, if the base field is $\mathbf {Q}_p$, this cohomology encodes the $p$-adic local Langlands correspondence for $2$-dimensional de Rham representations (of weight $0$ and $1$).

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