We are grateful to Tommaso de Fernex and János Kollár for helpful discussions. This joint work was started when both of the authors attended the conference Arithmetic Algebraic Geometry held in Berlin in June 2013. We thank the organizers, especially Hélène Esnault, for the hospitality. JN is partially supported by the ERC Starting Grant MOTZETA. CX is partially supported by the grant ‘Recruitment Program of Global Experts’.