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

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

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Bibliographic Details
Published in:Journal of the American Mathematical Society 2020-04, Vol.33 (2), p.311-362
Main Authors: Colmez, Pierre, Dospinescu, Gabriel, Nizioł, Wiesława
Format: Article
Language:English
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Summary:We compute the p p -adic geometric étale cohomology of the coverings of the Drinfeld half-plane, and we show that, if the base field is Q p \mathbf {Q}_p , this cohomology encodes the p p -adic local Langlands correspondence for 2 2 -dimensional de Rham representations (of weight 0 0 and 1 1 ).
ISSN:0894-0347
1088-6834
DOI:10.1090/jams/935