Existence of non-elliptic mod l Galois representations for every l >5

Luis Dieulefait

Existence of non-elliptic mod l Galois representations for every l >5

Number Theory 2007-05-23 v1

Authors: Luis Dieulefait

Abstract

For $\ell = 3$ and 5 it is known that every odd, irreducible, 2-dimensional representation of $\Gal(\bar{\Q}/\Q)$ with values in $\F_\ell$ and determinant equal to the cyclotomic character must "come from" the $\ell$ -torsion points of an elliptic curve defined over $\Q$ . We prove, by giving concrete counter-examples, that this result is false for every prime $\ell >5$ .

Keywords

galois representations mod l representations elliptic curves cyclotomic character counter-examples

Cite

@article{arxiv.math/0404025,
  title  = {Existence of non-elliptic mod l Galois representations for every l >5},
  author = {Luis Dieulefait},
  journal= {arXiv preprint arXiv:math/0404025},
  year   = {2007}
}

Related papers

View all related →