## Geometry Seminar - Abstracts

### Talk

Wednesday 22 March 2017, 16:00-17:00 in HG03.085

**Marta Pieropan** (FU Berlin)

*On rationally connected varieties over large C_1 fields of characteristic 0*

### Abstract

In the 1950s Lang studied the properties of C_1 fields, that is, fields
over which every hypersurface of degree at most n in an n-dimensional
projective space has a rational point. Later he conjectured that every
smooth proper rationally connected variety over a C_1 field has a rational
point. The conjecture is proven for finite fields (Esnault) and function
fields of curves over algebraically closed fields (Graber-Harris-de
Jong-Starr). I use birational geometry to address the open case of
Henselian fields of mixed characteristic with algebraically closed residue
field.

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