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La structure des représentations universelles modulo p pour gl2 by Morra-S

La structure des représentations universelles modulo p pour gl2

by Morra-S
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Book cover type: Paperback
  • ISBN13: 9786131576157
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 220
  • Original Price: GBP 61.0
  • Language: French
  • Edition: N/A
  • Item Weight: 327 grams
  • BISAC Subject(s): Arithmetic

Le programme de Langlands locale p-adique proposé par Breuil est un sujet en plein développement. Son établissement dans le cas particulier de GL2(Qp) (Berger, Breuil, Colmez, Emerton, Kisin, Paskunas...) a permis la résolution des conjectures profondes de géométrie arithmétique (Fontaine-Mazur, Breuil-Mézard...). N'est pas claire comment étendre ces résultats à des groupes plus généraux et un parmi le problèmes le plus troublants est du à une compréhension insuffisante des représentations modulaires en l=p de GL2. Dans ce travail nous avons pour objectif l'étude profond des objets universels de GL2. Nous proposons une méthode, égalément valable pour Qp et pour ses extensions non ramifiés, qui permet de comprendre la structure interne des ces objets. Cela repose sur un étude soigneuse de certaines séries de Fourier discrètes sur l'arbre de GL2 et de certains polynômes de Witt. On obtient une description optimale de la restriction des représentations supersingulières au compact maximal et aux sous-groupes de Cartan, et on montre l'existence d'un objet combinatoire simple (la structure euclidienne) qui contrôle la combinatoire interne des représentations universelles pour GL2.

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