August 18, 2020 article Open access Aachen paper

Elliptic curves over totally real cubic fields are modular

Algebra & Number Theory, vol. 14, pp. 1791–1800

DOI: 10.2140/ant.2020.14.1791 Full text (OA) OpenAlex

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.

Authors 2

Maarten Derickx Aachen Mathematisch Instituut

Leiden University

Affiliation as printed

Mathematisch Instituut, Universiteit Leiden, Netherlands
Samir Siksek

University of Warwick

Affiliation as printed

Mathematics Institute, University of Warwick, Coventry, United Kingdom

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