Article · Wikipedia archive · Last revised Aug 1, 2026

Châtelet surface

In algebraic geometry, a Châtelet surface is a rational surface studied by Châtelet given by an equation

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Aug 1, 2026

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≈ 1 min

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Some snapshots showing the real points of the Châtelet surface with P(x) = x³ – 5x² – 6x. Axes: x = red, y = yellow, z = blue source ↗

In algebraic geometry, a Châtelet surface is a rational surface studied by Châtelet (1959) given by an equation

y^{2}-az^{2}=P(x),\,

where P has degree 3 or 4. They are conic bundles.

References

References

Châtelet, F. (1959), "Points rationnels sur certaines courbes et surfaces cubiques", L'Enseignement mathématique, 2nd ser. (in French), 5: 153–170, MR 0130218, archived from the original on 2014-04-19, retrieved 2009-06-23
Viray, Bianca (2012), "Failure of the Hasse principle for Châtelet surfaces in characteristic 2", Journal de Théorie des Nombres de Bordeaux , 24 (1): 231–236, arXiv:0902.3644, doi:10.5802/jtnb.794, MR 2914907, S2CID 13878632