The modularity of elliptic curves over all but finitely many totally real fields of degree 5
The modularity of elliptic curves over all but finitely many totally real fields of degree 5
复制标题
椭圆曲线在除有限多个 5 次全实数域外的所有域上的模性
DOI：
10.1007/s40993-022-00383-0
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Sho Yoshikawa
中科院分区：
文献类型：
--
作者：
Yasuhiro Ishitsuka;Tetsushi Ito;Sho Yoshikawa
研究了某些模曲线上低阶点的有限性及其Atkin-Lehner等价性，作为应用，证明了除1000个5次全真实的域之外的所有域上椭圆曲线的模性.同时，利用Abramovich-Harris和Faltings关于Jacobian子簇的结果，证明了数域上大亏格曲线上5次有理点有限的一个判别准则.
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.