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题目：Torsion points of abelian varieties over large fields

报告人：段炼   博士 （科罗拉多州立大学）

时间：2021年11月21日（星期天）上午9:30-10:30

地点：腾讯会议  会议 ID：864 351 993

Abstract: Given an abelian variety A defined over a number field k. The classical Mordell-Weil theorem tells that the torsion group A(F)_{tors} is finite for any finite extension F/k. On the other hand, when F is the algebraic closure of k, then A(F)_{tors} is infinite. So what about the size of A(F)_{tors} for other infinite extensions F/k? In a work of Ribet in 1981, he proved that when F is the compositum of k and the maximal abelian extension Q^{ab} of Q, then A(F)_{tors} is always finite. In this talk, we will look at Ribet's result from a geometric point of view and try to understand it in terms of the relation of the torsion fields for a pair of group schemes. We will introduce our conjecture based on this observation, and review the known cases and counterexamples of this conjecture. At last, we will report our current progress in studying this conjecture. This is an ongoing project joint with Jeff Achter, Yuan Ren and Xiyuan Wang.

联系人：杨丽萍

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