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


Authors: Pierre Colmez, Gabriel Dospinescu and Wiesława Nizioł
Journal: J. Amer. Math. Soc. 33 (2020), 311-362
MSC (2010): Primary 11E95, 11F80, 11F85, 14G35, 14H99, 20G25, 22E35
DOI: https://doi.org/10.1090/jams/935
Published electronically: December 24, 2019
MathSciNet review: 4073863
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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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Additional Information

Pierre Colmez
Affiliation: CNRS, IMJ-PRG, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
Email: pierre.colmez@imj-prg.fr

Gabriel Dospinescu
Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 46 allée d’Italie, 69007 Lyon, France
Email: gabriel.dospinescu@ens-lyon.fr

Wiesława Nizioł
Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 46 allée d’Italie, 69007 Lyon, France
Email: wieslawa.niziol@ens-lyon.fr

DOI: https://doi.org/10.1090/jams/935
Received by editor(s): May 24, 2017
Received by editor(s) in revised form: August 5, 2019
Published electronically: December 24, 2019
Additional Notes: Les trois auteurs étaient membres des projets PERCOLATOR puis COLOSS de l’ANR pendant la complétion de ce travail
Dedicated: À la mémoire de Jean-Marc Fontaine
Article copyright: © Copyright 2019 American Mathematical Society