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The Modularity of Elliptic Curves Over All but Finitely Many Totally Real Fields of Degree 5 by Ishitsuka, Yasuhiro; Ito, Tetsushi; Yoshikawa, Sho is a scholarly article available to read on EtoBox.

What is The Modularity of Elliptic Curves Over All but Finitely Many Totally Real Fields of Degree 5 about?

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.

Author

Ishitsuka, Yasuhiro; Ito, Tetsushi; Yoshikawa, Sho

Published

2021

Language

EN