Title: Torsion points of abelian varieties over torsion fields
Speaker: Xiyuan Wang (OSU)
Speaker's URL: https://www.xiyuanwang.website/
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 $K^alg$, the torsion subgroup of $A(K^alg)$ 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.
URL associated with Seminar: https://research.math.osu.edu/agseminar/