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1997

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/16915

Galois representations, embedding problems and modular forms

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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.

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Teoria de Galois

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Galois theory

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CRESPO VICENTE, Teresa. Galois representations, embedding problems and modular forms. Collectanea Mathematica. 1997. Vol. 48, num. 1-2, pags. 63-83. ISSN 0010-0757. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/16915

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