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2004 Existence of Nonelliptic mod ${\ell}$ Galois Representations for Every $\ell > 5$
Luis Dieulefait
Experiment. Math. 13(3): 327-329 (2004).

Abstract

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 $\ell > 5$.

Citation

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Luis Dieulefait. "Existence of Nonelliptic mod ${\ell}$ Galois Representations for Every $\ell > 5$." Experiment. Math. 13 (3) 327 - 329, 2004.

Information

Published: 2004
First available in Project Euclid: 22 December 2004

zbMATH: 1091.11018
MathSciNet: MR2103330

Subjects:
Primary: 11G05
Secondary: 11F80

Keywords: Elliptic curves , Galois representations

Rights: Copyright © 2004 A K Peters, Ltd.

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Vol.13 • No. 3 • 2004
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