Weak approximation for cubic hypersurfaces
Weak approximation for cubic hypersurfaces

Zhiyu Tian , California Institute of Technology
Fine Hall 322
Given an algebraic variety X over a field F (e.g. number fields, function fields), a natural question is whether the set of rational points X(F) is nonempty. And if it is nonempty, how many rational points are there? In particular, are they Zariski dense? Do they satisfy weak approximation? For cubic hypersurfaces defined over the function field of a complex curve, we know the existence of rational points by Tsen' s theorem or the GraberHarrisStarr theorem. In this talk, I will discuss the weak approximation property of such hypersurfaces.