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

Luis V. Dieulefait

Displaying similar documents to “Newforms, inner twists, and the inverse Galois problem for projective linear groups”

Dihedral Galois representations and Katz modular forms.

Wiese, Gabor (2004)

Documenta Mathematica

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On a problem of Schinzel concerning principal divisors in arithmetic progressions

Charles Parry (1971)

Acta Arithmetica

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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,...

Modularity of an odd icosahedral representation

Arnaud Jehanne, Michael Müller (2000)

Journal de théorie des nombres de Bordeaux

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In this paper, we prove that the representation $ρ$ from $G_{ℚ}$ in GL $_{2} (ℂ)$ with image $A_{5}$ in PGL $_{2} (A_{5})$ corresponding to the example $16$ in [B-K] is modular. This representation has conductor $5203$ and determinant $χ_{- 43}$ ; its modularity was not yet proved, since this representation does not satisfy the hypothesis of the theorems of [B-D-SB-T] and [Tay2].

Representation of prime powers in arithmetical progressions by binary quadratic forms

Franz Halter-Koch (2003)

Journal de théorie des nombres de Bordeaux

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Let $Γ$ be a set of binary quadratic forms of the same discriminant, $Δ$ a set of arithmetical progressions and $m$ a positive integer. We investigate the representability of prime powers $p^{m}$ lying in some progression from $Δ$ by some form from $Γ$ .