报告题目: Torsion points in families of abelian varieties
报告人：高紫阳(Leibniz Universität Hannover)
时间： 2022-09-28 16:30-17:30
地点: 腾讯会议445-898-729 Password:072938
邀请人：孙鹏
报告摘要: Given an abelian scheme defined over \IQbar and an irreducible subvariety X which dominates the base, the Relative Manin-Mumford Conjecture (inspired by S.Zhang and proposed by Zannier) predicts how torsion points in closed fibers lie on X. The conjecture says that if such torsion points are Zariski dense in X, then the dimension of X is at least the relative dimension of the abelian scheme, unless X is contained in a proper subgroup scheme. In this talk, I will present a proof of this conjecture. As a consequence this gives a new proof of the Uniform Manin-Mumford Conjecture for curves (recently proved by Kühne) without using equidistribution. This is joint work with Philipp Habegger.
报告人简介：高紫阳，2010年本科毕业于北京大学，2015年获法国巴黎十一大和荷兰莱顿大学联合培养博士学位，现任德国汉诺威大学算术与几何首席（W3）教授,主要从事算术几何的理论研究。主要学术成果有：混合情形的Andr´e–Oort猜想，函数域上的Bogomolov猜想，曲线有理点的Mordell-Lang一致界等结果，相关成果发表于Ann. of Math.、Duke Math. J.、Crelle's journal等著名期刊。2022年获第二届DAVID GOSS奖。
