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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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 HTML | PDF
J. Amer. Math. Soc. 33 (2020), 311-362 Request permission

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
  • MR Author ID: 50720
  • Email: pierre.colmez@imj-prg.fr
  • Gabriel Dospinescu
  • Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 46 allée d’Italie, 69007 Lyon, France
  • MR Author ID: 857587
  • 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
  • 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
  • © Copyright 2019 American Mathematical Society
  • 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
  • MathSciNet review: 4073863