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Minimal lifts of dihedral 2-dimensional Galois representations

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Abstract

In this paper we study the connection between odd dihedral 2-dimensional modulo p Galois representations and modular forms with complex multiplication. More precisely, we prove that, for every such representation satisfying some explicit conditions, there exists a modular form giving rise to it of the type given by Serre’s conjecture (in its strong version) with the additional property of having complex multiplication.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, E-08007, Barcelona, Spain

    Joan Nualart

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  1. Joan Nualart
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Correspondence to Joan Nualart.

Additional information

Partially supported by a grant FPU (AP2005-1875) from Ministerio de Ciencia y Tecnología and by MTM2006-04895.

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Nualart, J. Minimal lifts of dihedral 2-dimensional Galois representations. Bull Braz Math Soc, New Series 42, 359–371 (2011). https://doi.org/10.1007/s00574-011-0020-9

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  • DOI: https://doi.org/10.1007/s00574-011-0020-9

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