Speaker：Xiyuan Wang (The Ohio State University)

Time：2023-5-2, 11:00

Location：Zoom Meeting ID：968 0121 1012（Password: 111111）

Abstract:

Let A be an abelian variety defined over a number field K. The well-known Mordell-Weil theorem states that for any finite extension L/K, the torsion subgroup of A(K) is finite. However, over the algebraic closure Kalg, the torsion subgroup of A(Kalg) is infinite. Therefore, a natural question arises: does the finiteness property of the torsion subgroup of A(L) hold for various infinite algebraic extensions L/K? In this talk, we will explore this question in the context where L is the "torsion field" of a different abelian variety. This is joint work with Jeff Achter and Lian Duan. If time permits, we will also formulate this question in a much more general setting and try to ask some new questions.