Tingxiang Zou，University of Münster

A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational points of a difference variety, namely a system of difference equations, in a finite field with a distinguished power of Frobenius. Like algebraic geometry, one can assign a dimension, called transformal dimension, to a difference variety. I will present a result which is a difference version of the Lang-Weil estimate with respect to the transformal dimension. This is joint work with Martin Hils, Ehud Hrushovski and Jinhe Ye.