On the image of Λ-adic Galois representations
Annales de l'Institut Fourier, Volume 52 (2002) no. 2, pp. 351-378.

We explore the question of how big the image of a Galois representation attached to a Λ-adic modular form with no complex multiplication is and show that for a “generic” set of Λ-adic modular forms (normalized, ordinary eigenforms with no complex multiplication), all have a large image.

Nous explorons la question de détermination de l’image des représentations galoisiennes modulaires Λ-adiques sans multiplication complexe et montrons que pour un ensemble “générique” de formes modulaires Λ-adiques (formes propres normalisées sans multiplication complexe), elles ont toutes une image contenant SL 2 (Λ).

DOI: 10.5802/aif.1890
Classification: 11F80, 11F11, 11F85, 11R23
Keywords: modular form, $p$-adic family, Galois representation, $p$-adic modular form
Mot clés : forme modulaire, famille $p$-adique, représentation galoisienne, forme modulaire $p$-adique
Fischman, Ami 1

1 517 N 137th Street, Seattle WA 98133 (USA)
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Fischman, Ami. On the image of $\Lambda $-adic Galois representations. Annales de l'Institut Fourier, Volume 52 (2002) no. 2, pp. 351-378. doi : 10.5802/aif.1890. http://www.numdam.org/articles/10.5802/aif.1890/

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