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Currently displaying 1 – 2 of 2

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Random Galois extensions of Hilbertian fields

Lior Bary-Soroker; Arno Fehm — 2013

Journal de Théorie des Nombres de Bordeaux

Let $L$ be a Galois extension of a countable Hilbertian field $K$ . Although $L$ need not be Hilbertian, we prove that an abundance of large Galois subextensions of $L / K$ are.

On varieties of Hilbert type

Lior Bary-Soroker; Arno Fehm; Sebastian Petersen — 2014

Annales de l’institut Fourier

A variety $X$ over a field $K$ is of Hilbert type if $X (K)$ is not thin. We prove that if $f : X \to S$ is a dominant morphism of $K$ -varieties and both $S$ and all fibers $f^{- 1} (s)$ , $s \in S (K)$ , 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.

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