Elliptic curves over totally real cubic fields are modular

Derickx, Maarten; Najman, Filip; Siksek, Samir

doi:10.2140/ant.2020.14.1791

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Elliptic curves over totally real cubic fields are modular

Maarten Derickx, Filip Najman and Samir Siksek

Vol. 14 (2020), No. 7, 1791–1800

DOI: 10.2140/ant.2020.14.1791

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.

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Keywords

modularity, elliptic curves, totally real fields

Mathematical Subject Classification 2010

Primary: 11F80

Secondary: 11G05

Milestones

Received: 10 January 2019

Revised: 11 July 2019

Accepted: 10 March 2020

Published: 18 August 2020

Authors

Maarten Derickx
Mathematisch Instituut Universiteit Leiden Netherlands

Filip Najman
Faculty of Science, Department of Mathematics University of Zagreb Croatia

Samir Siksek
Mathematics Institute University of Warwick Coventry United Kingdom

Vol. 14, No. 7, 2020