Lifting Galois Representations in a Conjecture of Figueiredo
type: CreativeWork
description: 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.
abstract: 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.
author: Rosengren, Wayne Bennett
language: English
keywords: Galois representations, Serre's Conjecture, Figueiredo, Mathematics
date modified: 2026-07-24T01:29:12Z
provider: Brigham Young University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Brigham Young University - Provo