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

Yasuhiro Ishitsuka, Tetsushi Ito, Sho Yoshikawa

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number82
JournalResearch in Number Theory
Volume8
Issue number4
DOIs
Publication statusPublished - Dec 2022

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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