Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Orateur(s) L. Dieulefait - ,
Titre Uniformity for families of Galois representations of Siegel modular forms
Date06/01/2003
Horaire14:00 à 16:00
RésumeWe consider symplectic four-dimensional Galois representations asthose attached by Taylor and Weissauer to level 1 Siegel cusp forms.Weprove that, under certain conditions, the images of these representationswill be generically the maximal possible symplectic group. We provethatall the family is reducible only for Saito-Kurokawa forms. Finally,weprove the following uniformity principle: if one of the representationsinthe family is reducible (for a prime p bigger than 4 times the weight)then almost all the representations in the family are reducible. Thislastresult gives evidence for Tate's conjecture on the Siegel threefoldand(for the irreducible components of the reducible Galois representation)for the existence of compatible families containing a given "geometric"Galois representation (even in cases not covered by Taylor's resultsonthe Fontaine-Mazur conjecture).
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