Mathematical Research Letters

Volume 25 (2018)

Number 2

Abelian Calabi–Yau threefolds: Néron models and rational points

Pages: 367 – 392



Fedor Bogomolov (Courant Institute, New York University, New York, N.Y., U.S.A.; and Higher School of Economics, National Research University, Russian Federation)

Lars Halvard Halle (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Fabien Pazuki (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Sho Tanimoto (Department of Mathematics, Faculty of Science, Kumamoto University, Kumamoto, Japan)


We study arithmetic properties of Calabi–Yau threefolds fibered by abelian surfaces: their Néron models and potential density of rational points.

The authors would like to thank Brendan Hassett for useful discussions and invaluable inputs. The authors would also like to thank anonymous referees for suggestions to improve their paper. The first author was partially supported by the Russian Academic Excellence Project ‘5-100’, by Simons Travel Grant, and by EPSRC programme grant “EP/M024830”. The third author is supported by ANR-14-CE25-0015 Gardio. The last three authors are supported by Lars Hesselholt’s Niels Bohr Professorship.

Received 9 December 2016

Accepted 17 July 2017

Published 5 July 2018