##### Department of Mathematics,

University of California San Diego

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### 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.

Host: James McKernan

### March 7, 2014

### 1:30 PM

### AP&M 7218

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