Duke Mathematical Journal
- Duke Math. J.
- Volume 109, Number 1 (2001), 97-122.
On the modularity of ℚ-curves
A ℚ-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its Galois conjugates. K. Ribet  asked whether every ℚ-curve is modular, and he showed that a positive answer would follow from J.-P. Serre's conjecture on mod p Galois representations. We answer Ribet's question in the affirmative, subject to certain local conditions at 3.
Duke Math. J., Volume 109, Number 1 (2001), 97-122.
First available in Project Euclid: 5 August 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 11F80: Galois representations 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 14G25: Global ground fields 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx]
Ellenberg, Jordan S.; Skinner, Chris. On the modularity of ℚ-curves. Duke Math. J. 109 (2001), no. 1, 97--122. doi:10.1215/S0012-7094-01-10914-9. https://projecteuclid.org/euclid.dmj/1091737223