The modularity of elliptic curves over all but finitely many totally real fields of degree 5

被引：0
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作者：
Yasuhiro Ishitsuka
Tetsushi Ito
Sho Yoshikawa
机构：
[1] Kyushu University,Institute of Mathematics for Industry
[2] Kyoto University,Department of Mathematics, Faculty of Science
[3] Gakushuin University,Department of Mathematics
来源：
Research in Number Theory | 2022年 / 8卷
关键词：
Modularity; Elliptic curves; Totally real fields; Modular curves; Modular forms; Jacobians;
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摘要：
We study the finiteness of low degree points on certain modular curves and their Atkin–Lehner quotients, and, as an application, prove the modularity of elliptic curves over all but finitely many totally real fields of degree 5. On the way, we prove a criterion for the finiteness of rational points of degree 5 on a curve of large genus over a number field using the results of Abramovich–Harris and Faltings on subvarieties of Jacobians.
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