Elliptic Curves over Totally Real Cubic Fields are Modular
Number Theory
2020-08-26 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1901.03436,
title = {Elliptic Curves over Totally Real Cubic Fields are Modular},
author = {Maarten Derickx and Filip Najman and Samir Siksek},
journal= {arXiv preprint arXiv:1901.03436},
year = {2020}
}