Lifting Galois Representations in a Conjecture of Figueiredo

<p>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.</p>

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Rosengren, Wayne Bennett

• Galois representations
• Serre's Conjecture
• Figueiredo
• Mathematics

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/1401

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-2400