Revistes Catalanes amb Accés Obert (RACO)

Galois representations, embedding problems and modular forms

Teresa Crespo Vicente

Resum


To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field $\mathbb{Q}$ 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.\newline 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.

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