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Diagrammes de Diamond et (φ, Γ)-modules

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Résumé

Let ρ be a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ p /ℚ p ) over ̅F p . The modulo p Langlands correspondence for GL2(ℚ p ) defined in [5], as realized in [9], can be reformulated as a quite simple recipee giving back the (φ, Γ)-module of the dual of ρ starting from the “Diamond diagram” associated to ρ. Let F be a finite unramified extension of ℚ p and ρ a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ p /F) over ̅F p . When one formally extends this recipee to the Diamond diagrams associated to ρ in [6], we show that one essentially finds the (φ, Γ)-module of the tensor induction from F to ℚ p of the dual of ρ.

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Authors and Affiliations

  1. C.N.R.S. & I.H.É.S. Le Bois-Marie, 35 route de Chartres, 91440, Bures-sur-Yvette, France

    Christophe Breuil

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  1. Christophe Breuil
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Correspondence to Christophe Breuil.

Additional information

Cet article fait suite à un travail en collaboration avec V. Paškūnas ([6]) et l’auteur remercie ce dernier pour lui avoir appris l’importance des sommes (2) ci-après. Il remercie L. Berger pour son intérêt et ses remarques concernant la partie 3. Il remercie enfin J. de Jong et P. Cartier pour d’agréables discussions à Columbia et à l’I.H.É.S. sur le théorème 7.1 et la remarque qui suit.

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Breuil, C. Diagrammes de Diamond et (φ, Γ)-modules. Isr. J. Math. 182, 349–382 (2011). https://doi.org/10.1007/s11856-011-0035-3

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  • DOI: https://doi.org/10.1007/s11856-011-0035-3

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