Galois representations, embedding problems and modular forms.

Crespo, Teresa. "Galois representations, embedding problems and modular forms.." Collectanea Mathematica 48.1-2 (1997): 63-83. <http://eudml.org/doc/40492>.

@article{Crespo1997,
abstract = {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 representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.},
author = {Crespo, Teresa},
journal = {Collectanea Mathematica},
keywords = {Grupo de Galois; Representación de grupos; Formas modulares; Estructuras proyectivas; Inmersiones e inclusiones en variedades; Números racionales; Clifford algebras; spinor norm; Artin -series; modular form of weight 1; Galois embedding problems; liftings of projective representations; orthogonal Galois representations},
language = {eng},
number = {1-2},
pages = {63-83},
title = {Galois representations, embedding problems and modular forms.},
url = {http://eudml.org/doc/40492},
volume = {48},
year = {1997},
}

TY - JOUR
AU - Crespo, Teresa
TI - Galois representations, embedding problems and modular forms.
JO - Collectanea Mathematica
PY - 1997
VL - 48
IS - 1-2
SP - 63
EP - 83
AB - 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 representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.
LA - eng
KW - Grupo de Galois; Representación de grupos; Formas modulares; Estructuras proyectivas; Inmersiones e inclusiones en variedades; Números racionales; Clifford algebras; spinor norm; Artin -series; modular form of weight 1; Galois embedding problems; liftings of projective representations; orthogonal Galois representations
UR - http://eudml.org/doc/40492
ER -