Wojciech J. Gajda

We report on a new fibration theorem in the context of varieties with the weak Hilbert property. Let Y, Z be smooth connected varieties over a field K of characteristic zero and f : Y → Z a fibration in the sense of Friedlander. Assume that Z has the Hilbert property and that the generic fibre of f has the weak Hilbert property. Then Y has the weak Hilbert property. This can be used to prove that certain abelian schemes over number fields have the Hilbert property.