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15 July 2001 On the modularity of ℚ-curves
Jordan S. Ellenberg, Chris Skinner
Duke Math. J. 109(1): 97-122 (15 July 2001). DOI: 10.1215/S0012-7094-01-10914-9

Abstract

A ℚ-curve is an elliptic curve over a number field K which is geometrically isogenous to each of its Galois conjugates. K. Ribet [17] 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.

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Jordan S. Ellenberg. Chris Skinner. "On the modularity of ℚ-curves." Duke Math. J. 109 (1) 97 - 122, 15 July 2001. https://doi.org/10.1215/S0012-7094-01-10914-9

Information

Published: 15 July 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1009.11038
MathSciNet: MR1844206
Digital Object Identifier: 10.1215/S0012-7094-01-10914-9

Subjects:
Primary: 11G05
Secondary: 11F80, 11G18, 14G25, 14H52

Rights: Copyright © 2001 Duke University Press

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Vol.109 • No. 1 • 15 July 2001
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