# Stefan Gille

### Chow motives of surfaces

**Abstract **: I will discuss some recent results on Chow-motives (with integral or finite coefficients) of surfaces. In particular I will introduce the upper motive of a geometrically rational surface which turns out to be a birational invariant. A further consequence of the results I present is that there are no phantom motives of dimension 0,1 or 2 in the category of Chow motives with integral coefficients.