On the local behaviour of ordinary $\Lambda $-adic representations

Eknath Ghate; Vinayak Vatsal

Displaying similar documents to “On the local behaviour of ordinary $Λ$ -adic 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 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.

On $p$ -adic $L$ -functions

John Coates (1988-1989)

Séminaire Bourbaki

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Motives over totally real fields and $p$ -adic $L$ -functions

Alexei A. Panchishkin (1994)

Annales de l'institut Fourier

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Special values of certain $L$ functions of the type $L (M, s)$ are studied where $M$ is a motive over a totally real field $F$ with coefficients in another field $T$ , and $L (M, s) = \prod_{𝔭} L_{𝔭} (M, 𝒩 𝔭^{- s})$ is an Euler product $𝔭$ running through maximal ideals of the maximal order $𝒪_{F}$ of $F$ and $\begin{matrix} L_{𝔭} (M, X)^{- 1} & = (1 - α^{(1)} (𝔭) X) \cdot (1 - α^{(2)} (𝔭) X) \cdot ... \cdot (1 - α (d) (𝔭) X) \\ = 1 + A_{1} (𝔭) X + ... + A_{d} (𝔭) X^{d} \end{matrix}$ being a polynomial with coefficients in $T$ . Using the Newton and the Hodge polygons of $M$ one formulate a conjectural criterium for the existence of a $p$ -adic analytic continuation of the special values....

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,...

Anti-cyclotomic Katz $p$ -adic $L$ -functions and congruence modules

H. Hida, J. Tilouine (1993)

Annales scientifiques de l'École Normale Supérieure

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Displaying similar documents to “On the local behaviour of ordinary Λ -adic 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 image of Λ -adic Galois representations

On p -adic L -functions

Motives over totally real fields and p -adic L -functions

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

Anti-cyclotomic Katz p -adic L -functions and congruence modules

Displaying similar documents to “On the local behaviour of ordinary $Λ$ -adic 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 image of $Λ$ -adic Galois representations

On $p$ -adic $L$ -functions

Motives over totally real fields and $p$ -adic $L$ -functions

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

Anti-cyclotomic Katz $p$ -adic $L$ -functions and congruence modules