Modularity of elliptic curves over abelian totally real fields unramified at 3, 5, and 7
Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 729-741.

Let K be a totally real field which is a finite abelian extension over and is unramified at 3,5, and 7. We prove that any elliptic curve E over K is modular, by reducing modularity of E to known modularity lifting theorems.

Soit K un corps totalement réel qui est une extension abélienne finie de non ramifiée en 3,5 et 7. Nous prouvons que toute courbe elliptique E sur K est modulaire, en réduisant la question de modularité de E aux théorèmes de relèvement modulaire connus.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.1047
Classification: 11F80,  11G05,  11F41
Keywords: elliptic curves, Hilbert modular forms, Galois representations
Sho Yoshikawa 1

1 Gakushuin University, Department of Mathematics, 1-5-1, Mejiro, Toshima-ku, Tokyo, Japan
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Sho Yoshikawa. Modularity of elliptic curves over abelian totally real fields unramified at 3, 5, and 7. Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 729-741. doi : 10.5802/jtnb.1047. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1047/

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