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Serre‘s Conjecture for Imaginary Quadratic Fields

Published online by Cambridge University Press:  04 December 2007

L. M. FIGUEIREDO
L. M. FIGUEIREDO
Affiliation:
Universidade Federal Fluminese, Instituto de Mathematica, Departamento de Geometria, Rua Ma‘ni Santos Braza, S/N Valonguinho, CEP 24020-005, Niteroi, RJ Brazil. e-mail: [email protected]
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Abstract

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We study an analog over an imaginary quadratic field K of Serre‘s conjecture for modular forms. Given a continuous irreducible representation ρ:Gal(Q/K) →GL$_2$(F$_l$) we ask if ρ is modular. We give three examples of representations ρ obtained by restriction of even representations of Gal(Q/Q). These representations appear to be modular when viewed as representations over K, as shown by the computer calculations described at the end of the paper.

Keywords

modular formsSerre‘s conjecture.
Type
Research Article
Information
Compositio Mathematica , Volume 118 , Issue 1 , August 1999 , pp. 103 - 122
Copyright
© 1999 Kluwer Academic Publishers