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Serre‘s Conjecture for Imaginary Quadratic Fields

Published online by Cambridge University Press:  04 December 2007

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: lmsf@impa.br
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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.

Type
Research Article
Copyright
© 1999 Kluwer Academic Publishers