Explicit determination of the images of the Galois representations attached to abelian surfaces with .

Dieulefait, Luis V.

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

Dihedral Galois representations and Katz modular forms.

Wiese, Gabor (2004)

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

Luis V. Dieulefait (2001)

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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...

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Modularity of Galois representations

Chris Skinner (2003)

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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.