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4:00 pm Tuesday, April 23, 2013 Algebraic Geometry Seminar: Weak approximation for cubic hypersurfacesby Zhiyu Tian (Caltech) in HB 227- 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.
Submitted by btl1@rice.edu |