Infinitely ramified Galois representations.

Ramakrishna, Ravi

Displaying similar documents to “Infinitely ramified Galois representations.”

Rings of integers of type $K (π, 1)$ .

Schmidt, Alexander (2007)

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Dihedral Galois representations and Katz modular forms.

Wiese, Gabor (2004)

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Wildly ramified Galois representations and a generalization of a conjecture of Serre.

Doud, Darrin (2005)

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${SL}_{3} (𝔽_{2})$ -extensions of $ℚ$ and arithmetic cohomology modulo 2.

Ash, Avner, Pollack, David, Soares, Dayna (2004)

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Refinement of Tate's discriminant bound and non-existence theorems for mod $p$ Galois representations.

Moon, Hyunsuk, Taguchi, Yuichiro (2003)

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On the meromorphic continuation of degree two $L$ -functions.

Taylor, Richard (2007)

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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.

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,...

Existence of nonelliptic mod $ℓ$ Galois representations for every $ℓ > 5$ .

Dieulefait, Luis (2004)

Experimental Mathematics

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Explicit determination of the images of the Galois representations attached to abelian surfaces with $End (A) = ℤ$ .

Dieulefait, Luis V. (2002)

Experimental Mathematics

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