第一类型课程的两个四分之一和两个五分之一交叉点
Intersections de deux quadriques et pinceaux de courbes de genre 1
摘要：
本研究专着着重于数域上曲面在射影直线上的亏格为1的曲线的算法，以及射影空间中两个二次曲面的交点的算法。前半部分采用并进一步发展了由Swinnerton-Dyer于1993年提出的技术，后来由Colliot-Thélène，Skorobogatov和Swinnerton-Dyer推广，用于研究亏格1曲线束上的有理点。下半年，建立在第一，是致力于四次del Pezzo表面和高维相交的两个二次曲面。在两个著名的命题（Schinzel假设和椭圆曲线的Tate-Shafarevich群的有限性）的基础上，它建立了两个n>2的二次曲面的所有光滑n维交点以及一大类4次del Pezzo曲面的Hasse原理。
英文摘要：
This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in projective space. The first half takes up and develops further the technique initiated by Swinnerton-Dyer in 1993, and later generalised by Colliot-Thélène, Skorobogatov and Swinnerton-Dyer, for studying rational points on pencils of curves of genus 1. The second half, which builds upon the first, is devoted to quartic del Pezzo surfaces and to higher-dimensional intersections of two quadrics. Conditionally on two well-known conjectures (Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups of elliptic curves), it establishes the Hasse principle for all smooth n-dimensional intersections of two quadrics with n>2 as well as for a large class of del Pezzo surfaces of degree 4.
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