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About Intersections de deux quadriques et pinceaux de courbes de genre 1: Intersections of two quadrics and pencils of curves of genus 1
Cet ouvrage est consacré � l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de la droite projective, et � l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une technique permettant d'étudier les points rationnels des pinceaux de courbes de genre 1. La première moitié de l'ouvrage reprend et développe cette technique ainsi que ses généralisations ultérieures. La seconde moitié, qui repose sur la première, porte sur les surfaces de del Pezzo de degré 4 et sur les intersections de deux quadriques de dimension supérieure; les résultats annoncés dans [C. R. Math. Acad. Sci. Paris 342 (2006), no. 4, 223--227] y sont démontrés.This research monograph focuses on the arithmetic, over number fields, ofsurfaces fibred into curves of genus 1 over the projective line, and ofintersections of two quadrics in projective space. The first half contains acomplete account of the technique initiated by Swinnerton-Dyer in 1993 forstudying rational points on pencils of curves of genus 1, while incorporatingand generalising most of its subsequent refinements. The second half, whichbuilds upon the first, is devoted to quartic del Pezzo surfaces andhigher-dimensional intersections of two quadrics. It culminates in the proofof the results announced in [C. R. Math. Acad. Sci. Paris 342 (2006), no. 4,223--227].
Detailed Information
| Author: | Olivier Wittenberg (auth.) |
|---|---|
| Publication Year: | 2007 |
| ISBN: | 3540691375 |
| Pages: | 227 |
| Language: | French |
| File Size: | 1.893 |
| Format: | |
| Price: | FREE |
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