Elliptic $\mod \ell$ Galois representations which are not minimally elliptic
Dieulefait, Luis
Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, p. 455-457 / Harvested from Project Euclid
In a recent preprint (see [C]), F. Calegari has shown that for $\ell = 2, 3, 5$ and $7$ there exist $2$-dimensional irreducible representations $\rho$ of Gal$(\bar{\Q}/\Q)$ with values in $\F_\ell$ coming from the $\ell$-torsion points of an elliptic curve defined over $\Q$, but not minimally, i.e., so that any elliptic curve giving rise to $\rho$ has prime-to-$\ell$ conductor greater than the (prime-to-$\ell$) conductor of $\rho$. In this brief note, we will show that the same is true for any prime $\ell >7$
Publié le : 2006-09-14
Classification: 
@article{1161350686,
     author = {Dieulefait, Luis},
     title = {Elliptic $\mod \ell$ Galois representations which are not minimally elliptic},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {12},
     number = {5},
     year = {2006},
     pages = { 455-457},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1161350686}
}
Dieulefait, Luis. Elliptic $\mod \ell$ Galois representations which are not minimally elliptic. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp.  455-457. http://gdmltest.u-ga.fr/item/1161350686/