ELLIPTIC CURVES OVER TOTALLY REAL QUARTIC FIELDS NOT CONTAINING √5 ARE MODULAR

被引：2

作者：

Box, Josha ^{[1
]}

机构：

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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 375卷 / 05期

关键词：

Elliptic curves; modularity; Chabauty; modular curves; ABELIAN-VARIETIES; RATIONAL-POINTS; TORSION POINTS; REPRESENTATIONS;

D O I：

10.1090/tran/8557

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that every elliptic curve defined over a totally real number field of degree 4 not containing root 5 is modular. To this end, we study the quartic points on four modular curves.

引用

页码：3129 / 3172

页数：44

共 50 条

[1] Elliptic curves over totally real cubic fields are modular
Derickx, Maarten
Najman, Filip
Siksek, Samir
[J]. ALGEBRA & NUMBER THEORY, 2020, 14 (07) : 1791 - 1800
[2] On the birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields
Longo, Matteo
[J]. ANNALES DE L INSTITUT FOURIER, 2006, 56 (03) : 689 - 733
[3] Elliptic curves over real quadratic fields are modular
Freitas, Nuno
Le Hung, Bao V.
Siksek, Samir
[J]. INVENTIONES MATHEMATICAE, 2015, 201 (01) : 159 - 206
[4] Elliptic curves over real quadratic fields are modular
Nuno Freitas
Bao V. Le Hung
Samir Siksek
[J]. Inventiones mathematicae, 2015, 201 : 159 - 206
[5] Darmon points on elliptic curves over totally real fields
Agashe, Amod
Trifkovic, Mak
[J]. JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2022, 37 (03) : 231 - 239
[6] EXCEPTIONAL ELLIPTIC CURVES OVER QUARTIC FIELDS
Najman, Filip
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (05) : 1231 - 1246
[7] An Algorithm for Modular Elliptic Curves over Real Quadratic Fields
Dembele, Lassina
[J]. EXPERIMENTAL MATHEMATICS, 2008, 17 (04) : 427 - 438
[8] Differential modular forms on Shimura curves over totally real fields
Banerjee, Debargha
[J]. JOURNAL OF NUMBER THEORY, 2014, 135 : 353 - 373
[9] Modularity of elliptic curves over abelian totally real fields unramified at 3, 5, and 7
Yoshikawa, Sho
[J]. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2018, 30 (03): : 729 - 741
[10] The modularity of elliptic curves over all but finitely many totally real fields of degree 5
Yasuhiro Ishitsuka
Tetsushi Ito
Sho Yoshikawa
[J]. Research in Number Theory, 2022, 8

← 1 2 3 4 5 →