Abstract
A variety X over a field Κ is of Hilbert type if X(Κ) is not thin. We prove that if f : X → S is a dominant morphism of Κ-varieties and both S and all fibers f-1(s), s ∈ S(Κ), are of Hilbert type, then so is X. We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Thélène and Sansuc on algebraic groups.
Original language | English |
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Pages (from-to) | 1893-1901 |
Number of pages | 9 |
Journal | Annales de l'Institut Fourier |
Volume | 64 |
Issue number | 5 |
DOIs | |
State | Published - 2014 |
Keywords
- Algebraic group
- Hilbertian field
- Thin set
- Variety of Hilbert type