中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 杨梓诠 博士（University of Wisconsin–Madison）

题  目：Some Recent Progress on the Tate and BSD Conjectures in Positive Characteristics

时  间：2023.09.15（星期五），09:00-10:00

地  点：Zoom会议：878 7991 3533   密码：0915

摘  要：I will report on some recent progress on the Tate and BSD conjectures in positive characteristics. Generalizing the case for K3 surfaces, we prove the Tate conjecture for all varieties with h^{2, 0} = 1 under a mild assumption on moduli. As an application,we prove the BSD conjecture for height 1 elliptic curves over function fields of genus 1. Time permitting, I will say a word on the relationship between the Tate/BSD conjecture and finiteness statements in arithmetic geometry. The main content is based ona joint work with Paul Hamacher and Xiaolei Zhao.