题目: Arithmetic purity of strong approximation and sieve methods

报告人: 黄治中，中科院数学所

时间: 2025年5月7日14:00-15:00

地点: 东区第五教学楼5107

摘要: Given a nice variety over a number field that satisfies strong approximation (i.e. rational points are dense in the adelic space), a question first proposed by O. Wittenberg asks whether this property holds true when one removes any Zariski closed subset of codimension at least two. We shall present several qualitative and quantitative positive answers to Wittenberg’s question. Our method combines effective counting results from homogeneous dynamics and various sieve methods, e.g. the affine linear sieve (developed by P. Sarnak et al.) and the geometric sieve (first discovered by T. Ekedahl). This is based on joint work in progress with Y. Cao (Jinan) and R. Zhang (Chongqing).