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# Châtelet surface

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

Châtelet, F. (1959), "Points rationnels sur certaines courbes et surfaces cubiques", L'Enseignement Mathématique. Revue Internationale. IIe Série 5: 153–170, MR 0130218

Viray, Bianca (2009), The Hasse principle for Chatelet surfaces in characteristic 2, arXiv:0902.3644

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