Zhiyu Tian

Given a system of polynomial equations with coefficients in a number field or a global function field, a natural question is to ask whether there is a solution over the same field. The Hasse principle, roughly speaking, says that there is a solution for the system of polynomial equations "globally" if there is a solution "everywhere locally", the latter of which is easy to check. In this talk, I will use the case of quadric hypersurfaces as an example to explain a geometric approach to proving this kind of statement for three classes of varieties defined over global function fields.