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On the local behaviour of ordinary Λ -adic representations

Eknath GhateVinayak Vatsal — 2004

Annales de l'Institut Fourier

Let f be a primitive cusp form of weight at least 2, and let ρ f be the p -adic Galois representation attached to f . If f is p -ordinary, then it is known that the restriction of ρ f 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...

On classical weight one forms in Hida families

Mladen DimitrovEknath Ghate — 2012

Journal de Théorie des Nombres de Bordeaux

We give precise estimates for the number of classical weight one specializations of a non-CM family of ordinary cuspidal eigenforms. We also provide examples to show how uniqueness fails with respect to membership of weight one forms in families.

Endomorphism algebras of motives attached to elliptic modular forms

Alexander F. BrownEknath P. Ghate — 2003

Annales de l’institut Fourier

We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra X . The Tate conjecture predicts that X is the full endomorphism algebra of the motive. We also investigate the Brauer class of X . For example we show that if the nebentypus is real and p is a prime that does not divide the level, then the local behaviour of X at a place lying above p is essentially determined...

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