-invariants, partially de Rham families, and local-global compatibility
[Invariants , familles partiellement de de Rham, et compatibilité local-global]
Annales de l'Institut Fourier, Tome 67 (2017) no. 4, pp. 1457-1519.

Soit F une extension finie de p . En étudiant des familles de représentations galoisiennes partiellement de de Rham, on donne une formule de Colmez–Greenberg–Stevens (concernant les invariants de Fontaine–Mazur) pour les représentations semi-stables non cristallines de dimension 2 de Gal( p ¯/F ). Comme application, on montre dans le cas critique des résultats de compatibilité local-global pour le H 1 -complété d’une courbe de Shimura quaternionique, et en particulier l’égalité des invariants de Fontaine–Mazur et Breuil.

Let F be a finite extension of p . By considering partially de Rham families, we establish a Colmez–Greenberg–Stevens formula (on Fontaine–Mazur -invariants) for (general) 2-dimensional semi-stable non-crystalline representations of the group Gal( p ¯/F ). As an application, we prove local-global compatibility results for completed cohomology of quaternion Shimura curves, and in particular the equality of Fontaine–Mazur -invariants and Breuil’s -invariants, in critical case.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/aif.3115
Classification : 11S37, 11S80, 22D12
Keywords: $\protect \mathcal{L}$-invariants, partially de Rham families, locally analytic representations, local-global compatibility
Mot clés : Invariants $\protect \mathcal{L}$, familles partiellement de de Rham, représentations localement analytiques, compatibilité local-global
Ding, Yiwen 1

1 Department of Mathematics Imperial College London Kensington, Londres SW7 2AZ (UK)
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Ding, Yiwen. $\protect \mathcal{L}$-invariants, partially de Rham families, and local-global compatibility. Annales de l'Institut Fourier, Tome 67 (2017) no. 4, pp. 1457-1519. doi : 10.5802/aif.3115. http://archive.numdam.org/articles/10.5802/aif.3115/

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