Mathematical Research Letters

Volume 27 (2020)

Number 1

Torsion of $\mathbb{Q}$-curves over quadratic fields

Pages: 209 – 225



Samuel Le Fourn (Mathematics Institute, University of Warwick, Coventry, United Kingdom)

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


We determine all the possible torsion groups of $\mathbb{Q}$‑curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.

Le Fourn was supported by the European Union’s Horizon 2020 research and programme under the Marie Sklodowska-Curie grant agreement No 793646, titled LowDegModCurve. Najman was supported by the QuantiXLie Centre of Excellence, a project co-financed by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (Grant KK. and by the Croatian Science Foundation under the project no. IP-2018-01-1313.

Received 20 March 2018

Accepted 1 February 2019

Published 8 April 2020