By Olivier Wittenberg
Cet ouvrage est consacré à l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de los angeles droite projective, et à l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une approach permettant d'étudier les issues rationnels des pinceaux de courbes de style 1. l. a. première moitié de l'ouvrage reprend et développe cette procedure ainsi que ses généralisations ultérieures. l. a. seconde moitié, qui repose sur l. a. première, porte sur les surfaces de del Pezzo de degré four et sur les intersections de deux quadriques de measurement supérieure; les résultats annoncés dans [C. R. Math. Acad. Sci. Paris 342 (2006), no. four, 223--227] y sont démontrés.
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