In 1987, Jean-Pierre Serre gave a conjecture on the correspondence between degree 2 odd irreducible representations of the absolute Galois group of Q and modular forms. Letting M be an imaginary quadratic field, L.M. Figueiredo gave a related conjecture concerning degree 2 irreducible representations of the absolute Galois group of M and their correspondence to homology classes. He experimentally confirmed his conjecture for three representations arising from PSL(2,3)-polynomials, but only up to a sign because he did not lift them to SL(2,3)-polynomials. In this paper we compute explicit lifts and give further evidence that his conjecture is accurate.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Rosengren, Wayne Bennett, "Lifting Galois Representations in a Conjecture of Figueiredo" (2008). All Theses and Dissertations. 1401.
Galois representations, Serre's Conjecture, Figueiredo