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.

中文翻译：

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全实三次域上的椭圆曲线是模块化的

我们证明了在完全实立方域上定义的所有椭圆曲线都是模的。这建立在 Freitas、Le Hung 和 Siksek 之前的工作之上，他们证明了椭圆曲线在实二次域上的模块化，以及最近由于 Thorne 和 Kalyanswamy 的突破。