Vol. 14, No. 7, 2020

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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.

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