Existence of Nonelliptic mod ${\ell}$ Galois Representations for Every $\ell > 5$

Dieulefait, Luis

Experiment. Math., Tome 13 (2004) no. 1, p. 327-329 / Harvested from Project Euclid

Résumé

For $\ell =$ 3 and 5 it is known that every odd, irreducible, two-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 $\ell > 5$.

Publié le : 2004-05-14
Classification: Elliptic curves, Galois representations, 11G05, 11F80

@article{1103749840,
     author = {Dieulefait, Luis},
     title = {Existence of Nonelliptic mod ${\ell}$ Galois Representations for Every $\ell > 5$},
     journal = {Experiment. Math.},
     volume = {13},
     number = {1},
     year = {2004},
     pages = { 327-329},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1103749840}
}

Dieulefait, Luis. Existence of Nonelliptic mod ${\ell}$ Galois Representations for Every $\ell > 5$. Experiment. Math., Tome 13 (2004) no. 1, pp.  327-329. http://gdmltest.u-ga.fr/item/1103749840/