Some snapshots showing the real points of the Châtelet surface with P(x)=x^3-5*x^2-6*x. Axis: x=red, y=yellow, z=blue In algebraic geometry , a Châtelet surface is a rational surface studied by Châtelet (1959 ) given by an equation
y
2
−
a
z
2
=
P
(
x
)
,
{\displaystyle 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 5 : 153–170, MR 0130218 , archived from the original on 2014-04-19, retrieved 2009-06-23Viray, 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 Categories :
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