Zhiyu Tian : Weak approximation for cubic hypersurfaces

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Feb. 26, 2014, 4 p.m.

In

SEO 427

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.