Elliptic Curves over Totally Real Cubic Fields are Modular

11 Jan 2019 · Derickx Maarten, Najman Filip, Siksek Samir ·

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.