Compositio Mathematica



Serre‘s Conjecture for Imaginary Quadratic Fields


L. M. FIGUEIREDO a1
a1 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

Article author query
figueiredo lm   [Google Scholar] 
 

Abstract

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) [rightward arrow]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.


Key Words: modular forms; Serre‘s conjecture.; ; ; .