Principe de Hasse, surfaces cubiques et inersections de deux quadriques. (Hasse principle, cubic surfaces and intersections of two quadrics). (French) Zbl 0661.14021

Journées arithmétiques, Besançon/France 1985, Astérisque 147/148, 183-207 (1987).
[For the entire collection see Zbl 0605.00004.]
This is a very nice survey of results of the author (many of them are jointly with J.-L. Colliot-Thélène) and of other mathematicians on the arithmetic of cubic surfaces, intersections of two quadrics and Châtelet surfaces. They are concentrated around the problem of the validity of the Hasse principle for such varieties. Full details for many new results have appeared recently in two papers of the author, J.- L. Colliot-Thélène and P. Swinnerton-Dyer [J. Reine Angew. Math. 373, 37-107 and 374, 72-168 (1987; Zbl 0622.14029 and Zbl 0622.14030)].
Reviewer: I.Dolgachev


14G25 Global ground fields in algebraic geometry
14G05 Rational points
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
11R99 Algebraic number theory: global fields