Elliptic Curves over Real Quadratic Fields are Modular

A Ogg; A Wiles; A Wiles; AV Sutherland; B Conrad; B Mazur; B Poonen; Bao V. Le Hung; C Breuil; C Khare; C Khare; C Skinner; D Blasius; E Halberstadt; F Diamond; F Jarvis; F Jarvis; G Faltings; H Carayol; H Carayol; J Ellenberg; J Harris; J Manoharmayum; J Tunnell; J-P Serre; JE Cremona; L Merel; M Kisin; M Stoll; M Stoll; Nuno Freitas; R Taylor; R Taylor; R Taylor; S Kamienny; S Siksek; S Siksek; Samir Siksek; T Barnet-Lamb; T Barnet-Lamb; T Fisher; T Gee; VI Danilov

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Elliptic Curves over Real Quadratic Fields are Modular

Abstract

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio

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