##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Morgan Brown

#### University of Miami

## Points on del Pezzo surfaces in mixed characteristic

##### Abstract:

The Graber-Harris-Starr theorem says that any family of smooth rationally connected varieties over a complex curve has a section. A natural analogue of this statement in mixed characteristic would be that every rationally connected variety over the maximal unramified extension of a p-adic field has a rational point. I will discuss a geometric approach to this problem, as well as a proof of this statement for del Pezzo surfaces (for ${p>3}$). This is joint work with David Zureick-Brown.

Host: James McKernan

### June 2, 2017

### 4:00 PM

### AP&M 5829

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