Weak approximation and rationally connected varieties over function fields of curves
arXiv:1008.2711
Abstract
This is a survey of weak approximation over complex function fields, touching on the Koll'ar-Miyaoka-Mori theorem, places of good and bad reduction, the special case of rational surfaces, rationally simply connected varieties, and applications to low-degree complete intersections.
49 pages; based on lectures given in Strasbourg in May 2008 at the Session Etats de la Recherche "Vari'et'es rationnellement connexes : aspects g'eom'etriques et arithm'etiques"