Displaying similar documents to “Companion forms and weight one forms.”

On the image of Λ -adic Galois representations

Ami Fischman (2002)

Annales de l’institut Fourier

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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.

Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture

Krzysztof Klosin (2009)

Annales de l’institut Fourier

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Let k be a positive integer divisible by 4, p > k a prime, f an elliptic cuspidal eigenform (ordinary at p ) of weight k - 1 , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives ad 0 M ( - 1 ) and ad 0 M ( 2 ) , where M is the motif attached to f . More precisely, we prove that under certain conditions the p -adic valuation of the algebraic part of the symmetric square L -function of f evaluated at k provides a lower bound for the p -adic valuation of the order...

Modularity of p -adic Galois representations via p -adic approximations

Chandrashekhar Khare (2004)

Journal de Théorie des Nombres de Bordeaux

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In this short note we give a new approach to proving modularity of p -adic Galois representations using a method of p -adic approximations. This recovers some of the well-known results of Wiles and Taylor in many, but not all, cases. A feature of the new approach is that it works directly with the p -adic Galois representation whose modularity is sought to be established. The three main ingredients are a Galois cohomology technique of Ramakrishna, a level raising result due to Ribet, Diamond,...