Colliot-Thélène–Sansuc conjecture on the Hilbert property of unirational varieties

Let $X$ be a unirational variety over a number field. The Colliot-Thélène–Sansuc conjecture. $X$ has the Hilbert property.

This conjecture connects the abundance of rational points with the inverse Galois problem. It is refuted: the paper notes that the relevant surface is not geometrically unirational, so the converse of the conjecture is false.