On the local behaviour of ordinary Λ-adic representations

Ghate, Eknath ; Vatsal, Vinayak (2004) On the local behaviour of ordinary Λ-adic representations Annales de L'Institut Fourier, 54 (7). pp. 2143-2162. ISSN 0373-0956

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Official URL: http://aif.cedram.org/aif-bin/item?id=AIF_2004__54...

Related URL: http://dx.doi.org/10.5802/aif.2077


Let f be a primitive cusp form of weight at least 2, and let ρf be the p-adic Galois representation attached to f. If f is p-ordinary, then it is known that the restriction of ρf to a decomposition group at p is “upper triangular”. If in addition f has CM, then this representation is even “diagonal”. In this paper we provide evidence for the converse. More precisely, we show that the local Galois representation is not diagonal, for all except possibly finitely many of the arithmetic members of a non-CM family of p-ordinary forms. We assume p is odd, and work under some technical conditions on the residual representation. We also settle the analogous question for p-ordinary Λ-adic forms, under similar conditions.

Item Type:Article
Source:Copyright of this article belongs to Association des Annales de l'Institut Fourier.
Keywords:Λ-Adic Forms; p-Adic Families; Ordinary Primes, Galois Representations
ID Code:101587
Deposited On:09 Mar 2018 10:34
Last Modified:09 Mar 2018 10:34

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