Experimental Mathematics

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

Luis Dieulefait

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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 $\ell > 5$.

Article information

Source
Experiment. Math., Volume 13, Issue 3 (2004), 327-329.

Dates
First available in Project Euclid: 22 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.em/1103749840

Mathematical Reviews number (MathSciNet)
MR2103330

Zentralblatt MATH identifier
1091.11018

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 11F80: Galois representations

Keywords
Elliptic curves Galois representations

Citation

Dieulefait, Luis. Existence of Nonelliptic mod ${\ell}$ Galois Representations for Every $\ell > 5$. Experiment. Math. 13 (2004), no. 3, 327--329. https://projecteuclid.org/euclid.em/1103749840


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