Elliptic curves over totally real cubic fields are modular

被引：15

作者：

Derickx, Maarten ^{[1
]}

Najman, Filip ^{[2
]}

Siksek, Samir ^{[3
]}

机构：

[1] Leiden Univ, Math Inst, Leiden, Netherlands

[2] Univ Zagreb, Fac Sci, Dept Math, Zagreb, Croatia

[3] Univ Warwick, Math Inst, Coventry, W Midlands, England

来源：

ALGEBRA & NUMBER THEORY | 2020年 / 14卷 / 07期

基金：

英国工程与自然科学研究理事会;

关键词：

modularity; elliptic curves; totally real fields; CONGRUENCES;

D O I：

10.2140/ant.2020.14.1791

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to Thorne and to Kalyanswamy.

引用

页码：1791 / 1800

页数：10

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