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Sur La Conjecture Principale Pour Les Corps CM by Mainardi-F

Sur La Conjecture Principale Pour Les Corps CM

by Mainardi-F
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Book cover type: Paperback
  • ISBN13: 9783841784766
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 144
  • Original Price: GBP 42.0
  • Language: French
  • Edition: N/A
  • Item Weight: 223 grams
  • BISAC Subject(s): Algebra / General

L'objectif de ce travail est d'une part de démontrer une relation de divisibilité, qui constitue une étape importante vers la démonstration de la conjecture principale pour les corps CM, et d'autre part d'étudier les représentations p-adiques admissibles des groupes unitaires en trois variables. On définit un idéal d'Eisenstein dans l'algèbre de Hecke quasi-ordinaire d'un groupe unitaire en trois variables; cet idéal 'mesure' les congruences entre formes automorphes cuspidales et une certaine série de Eisenstein. De telles congruences donnent lieu à des représentations Galoisiennes permettant de construire des éléments dans des groupes de Selmer. Une analyse fine des propriétés de ramification et de réductibilité des ces représentations permet de démontrer une partie de la conjecture. Les conducteurs locaux des représentations admissibles des groupes unitaires en trois variables sont aussi étudiés, généralisant ainsi des résultats bien connus dans le cas du groupe GL(2)

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