Hassett

Weak Approximation for Rationally Connected Varieties over Function Fields of Curves

Let B be a smooth complex curve and X a variety smooth and proper over C(B). Graber-Harris-Starr have shown that if X is geometrically rationally connected then X(C(B)) is nonempty. Building on work of Kollár-Miyaoka-Mori and others, we show that X satisfies weak approximation, at places of good reduction. We shall also discuss results at places of bad reduction in special cases like cubic surfaces. (joint work with Yuri Tschinkel)