数理逻辑研讨班：Number of rational points of difference varieties in finite difference fields

中科院数学与系统科学研究院

数学研究所

学术报告

数理逻辑研讨班

报告人：Tingxiang Zou（University of Münster）   

题  目：Number of rational points of difference  varieties in finite difference fields

时  间：2023.03.31（星期五）16:00-18:00

地  点：腾讯会议: 311-0934-3182

摘  要：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.