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

Chandrashekhar Khare

Displaying similar documents to “Modularity of $p$ -adic Galois representations via $p$ -adic approximations”

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 geometric representations of $G_{ℚ}$ .

Wintenberger, J.-P. (2007)

Documenta Mathematica

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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...

Newforms, inner twists, and the inverse Galois problem for projective linear groups

Luis V. Dieulefait (2001)

Journal de théorie des nombres de Bordeaux

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We reformulate more explicitly the results of Momose, Ribet and Papier concerning the images of the Galois representations attached to newforms without complex multiplication, restricted to the case of weight $2$ and trivial nebentypus. We compute two examples of these newforms, with a single inner twist, and we prove that for every inert prime greater than $3$ the image is as large as possible. As a consequence, we prove that the groups $PGL (2, 𝔽_{ℓ^{2}})$ for every prime $(ℓ \equiv 3, 5 (mod 8), ℓ > 3)$ , and $PGL (2, 𝔽_{ℓ^{5}})$ for every prime $ℓ \neg \equiv 0 \pm 1 (mod 11); ℓ > 3)$ , are...

Modularity of Galois representations

Chris Skinner (2003)

Journal de théorie des nombres de Bordeaux

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This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, $p$ -adic Galois representations associated to holomorphic Hilbert modular newforms.

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

B. Mazur (1990)

Compositio Mathematica

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On Galois representations defined by torsion points of modular elliptic curves

P. Bayer, J. C. Lario (1992)

Compositio Mathematica

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Sur la recherche des $p$ -extensions non ramifiées de $ℚ (μ_{p})$

Kenneth A. Ribet (1975-1976)

Groupe d'étude d'algèbre Groupe d'étude d'algèbre

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Displaying similar documents to “Modularity of p -adic Galois representations via p -adic approximations”

Displaying similar documents to “Modularity of $p$ -adic Galois representations via $p$ -adic approximations”