A family of varieties with exactly one pointless rational fiber
Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 741-745.

We construct a concrete example of a 1-parameter family of smooth projective geometrically integral varieties over an open subscheme of 1 such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.

On construit un exemple concret d’une famille à un paramètre de variétés lisses, projectives, et géométriquement intègres sur un sous-schéma ouvert de 1 , de sorte qu’il y ait précisément une fibre rationnelle sans point rationnel. Ceci rend explicite une construction de Poonen.

Received:
Published online:
DOI: 10.5802/jtnb.743
Bianca Viray 1

1 Mathematics Department Box 1917 Brown University Providence, RI 02912 USA
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Bianca Viray. A family of varieties with exactly one pointless rational fiber. Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 741-745. doi : 10.5802/jtnb.743. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.743/

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