Algebraic Geometry Seminar
Zhiyu Tian
Caltech
Weak approximation for cubic hypersurfaces
Abstract: 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 non-empty. And if it is non-empty, 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 Graber-Harris-Starr theorem. In this talk, I will discuss the weak approximation property of such hypersurfaces.
Wednesday February 26, 2014 at 4:00 PM in SEO 427