Lifting Galois Representations in a Conjecture of Figueiredo

Lifting Galois Representations in a Conjecture of Figueiredo

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 representation...

Full description

Bibliographic Details
Main Author: Rosengren, Wayne Bennett
Format: Others
Published: BYU ScholarsArchive 2008
Subjects:
Galois representations
Serre's Conjecture
Figueiredo
Mathematics
Online Access:https://scholarsarchive.byu.edu/etd/1401
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2400&context=etd
id ndltd-BGMYU2-oai-scholarsarchive.byu.edu-etd-2400
record_format oai_dc
spelling ndltd-BGMYU2-oai-scholarsarchive.byu.edu-etd-24002019-05-16T03:23:40Z Lifting Galois Representations in a Conjecture of Figueiredo Rosengren, Wayne Bennett 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. 2008-06-12T07:00:00Z text application/pdf https://scholarsarchive.byu.edu/etd/1401 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2400&context=etd http://lib.byu.edu/about/copyright/ All Theses and Dissertations BYU ScholarsArchive Galois representations Serre's Conjecture Figueiredo Mathematics
collection NDLTD
format Others
sources NDLTD
topic Galois representations
Serre's Conjecture
Figueiredo
Mathematics
spellingShingle Galois representations
Serre's Conjecture
Figueiredo
Mathematics
Rosengren, Wayne Bennett
Lifting Galois Representations in a Conjecture of Figueiredo
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.
author Rosengren, Wayne Bennett
author_facet Rosengren, Wayne Bennett
author_sort Rosengren, Wayne Bennett
title Lifting Galois Representations in a Conjecture of Figueiredo
title_short Lifting Galois Representations in a Conjecture of Figueiredo
title_full Lifting Galois Representations in a Conjecture of Figueiredo
title_fullStr Lifting Galois Representations in a Conjecture of Figueiredo
title_full_unstemmed Lifting Galois Representations in a Conjecture of Figueiredo
title_sort lifting galois representations in a conjecture of figueiredo
publisher BYU ScholarsArchive
publishDate 2008
url https://scholarsarchive.byu.edu/etd/1401
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2400&context=etd
work_keys_str_mv AT rosengrenwaynebennett liftinggaloisrepresentationsinaconjectureoffigueiredo
_version_ 1719185864611856384

Similar Items