On the image of $\Lambda $-adic Galois representations

Ami Fischman

Displaying similar documents to “On the image of $Λ$ -adic Galois representations”

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

Haruzo Hida (1996)

Mémoires de la Société Mathématique de France

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On the local behaviour of ordinary $Λ$ -adic representations

Eknath Ghate, Vinayak Vatsal (2004)

Annales de l'Institut Fourier

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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...

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,...

Two-dimensional $p$ -adic Galois representations unramified away from $p$

B. Mazur (1990)

Compositio Mathematica

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On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

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Let $D (s, f, g)$ be the Rankin product $L$ -function for two Hilbert cusp forms $f$ and $g$ . This $L$ -function is in fact the standard $L$ -function of an automorphic representation of the algebraic group $G L (2) \times G L (2)$ defined over a totally real field. Under the ordinarity assumption at a given prime $p$ for $f$ and $g$ , we shall construct a $p$ -adic analytic function of several variables which interpolates the algebraic part of $D (m, f, g)$ for critical integers $m$ , regarding all the ingredients $m$ , $f$ and $g$ as variables.

On $p$ -adic $L$ -functions

John Coates (1988-1989)

Séminaire Bourbaki

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Displaying similar documents to “On the image of Λ -adic Galois representations”

On the search of genuine p -adic modular L -functions for G L ( n ) . With a correction to: On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

On the local behaviour of ordinary Λ -adic representations

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

Two-dimensional p -adic Galois representations unramified away from p

On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

On p -adic L -functions

Displaying similar documents to “On the image of $Λ$ -adic Galois representations”

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

On the local behaviour of ordinary $Λ$ -adic representations

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

Two-dimensional $p$ -adic Galois representations unramified away from $p$

On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

On $p$ -adic $L$ -functions