Displaying similar documents to “Polynomials of Galois representations attached to elliptic curves.”

Differential Galois realization of double covers

Teresa Crespo, Zbigniew Hajto (2002)

Annales de l’institut Fourier

Similarity:

An effective construction of homogeneous linear differential equations of order 2 with Galois group 2 A 4 , 2 S 4 or 2 A 5 is presented.

On elliptic Galois representations and genus-zero modular units

Julio Fernández, Joan-C. Lario (2007)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Given an odd prime   p   and a representation ϱ   of the absolute Galois group of a number field k onto PGL 2 ( 𝔽 p ) with cyclotomic determinant, the moduli space of elliptic curves defined over k with p -torsion giving rise to ϱ consists of two twists of the modular curve X ( p ) . We make here explicit the only genus-zero cases p = 3 and p = 5 , which are also the only cases: PGL 2 ( 𝔽 p ) ≃ 𝒮 n for n = 4 or n = 5 , respectively. This is done by studying the corresponding twisted Galois actions on the function field of the curve, for which...

Galois representations, embedding problems and modular forms.

Teresa Crespo (1997)

Collectanea Mathematica

Similarity:

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective...

On the inverse problem of Galois theory.

Núria Vila (1992)

Publicacions Matemàtiques

Similarity:

The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.