【延期】On the torsion-finiteness over torsion extensions

：段炼（上海科技大学）
：2023-03-27 15:00
：海韵园数理大楼天元会议室686

报告人：段炼（上海科技大学）

时  间：2023年3月27日下午15:00-16:30

地  点：海韵园数理大楼天元会议室686

内容摘要: It is well known that over any number field, the Mordell Weil group of an abelian variety is finitely generated. Thus an abelian variety has only finitely many rational torsion points over a number field. This is in general not true if the base field is an infinite extension over Q. However, around 1981 Ribet proved that every abelian variety defined over a number field still has only finitely many torsion Q^ab-points, where Q^ab is the maximal abelian extension of Q. His result is then generalized by the works of Zarhin, Lombardo, and Rossler-Szamuely. In this talk, we will introduce another generalization of this result. That is, we will study the "torsion-finiteness" of an abelian variety over an infinite extension of the base field generated by adjoint all the torsion points of another abelian variety. Assuming the Mumford-Tate conjecture, we will give a criterion to the torsion-finiteness in terms of the Mumford-Tate groups of the related abelian varieties. In particular, when the conjecture is known, our theorem will deduce the unconditional results. This includes most cases of abelian varieties of dimension <=3 and the CM cases. If time allows, we will also talk about the analogue over function field. This is a joint work with Jeff Achter, Jiangxue Fang, Yuan Ren and Xiyuan Wang.

个人简介：

段炼，本科及硕士毕业于四川大学，后在马萨诸塞大学阿默斯特分校获得博士学位。曾于科罗拉多州立大学深造并于2022年入职上海科技大学数学科学研究所，担任助理教授职位。主要研究方向为算数几何，特别是Galois表示及其应用。 已在Math. Comp., Math. Res. Lett., J. Number Theory, Finite Fields Appl., Ramanujan J.等国际期刊上发表研究成果。

 

联系人：易少云