Weak approximation and rationally connected varieties over function fields of curves
This is a survey about weak approximations for rationally connected varieties over the function field of a complex curve.NEWLINENEWLINEThe author discusses general properties of weak approximation over function fields of a curve, and proves some partial results supporting his conjecture (with Y. Tschinkel) that weak approximation always holds for rationally connected varieties over the function field of a curve.NEWLINENEWLINEAmong the results proved in the survey are the followings: weak approximation at places of good reduction, for low degree hypersurfaces (at all places) and rationally simply connected varieties (at all places).NEWLINENEWLINEIn the appendix, the author discusses some properties of stable maps used in the proof.NEWLINENEWLINEFor the entire collection see [Zbl 1237.14006].
scientific article; zbMATH DE number 6077520
scientific article