Modularity of elliptic curves over abelian totally real fields unramified at 3, 5, and 7
Sho Yoshikawa1
1 Gakushuin University, Department of Mathematics, 1-5-1, Mejiro, Toshima-ku, Tokyo, Japan
Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 729-741.

Let K be a totally real field which is a finite abelian extension over ℚ 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 ℚ 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.

Reçu le :
Accepté le :
Publié le :
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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 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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  • Yasuhiro Ishitsuka; Tetsushi Ito; Sho Yoshikawa The modularity of elliptic curves over all but finitely many totally real fields of degree 5, Research in Number Theory, Volume 8 (2022) no. 4 | DOI:10.1007/s40993-022-00383-0
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