On Uniform Boundedness of Torsion Points for Abelian Varieties Over Function Fields

Let K be the function field of a smooth projective curve B over the complex numbers and let g be a positive integer. The uniform boundedness conjecture predicts that there exists a constant N, depending only on g and K, such that for any g-dimensional abelian variety A over K, any K-rational torsion point of A must have order at most N. In this talk, we will discuss some recent progress under the assumption that A has semistable reduction over K. This is joint work with Nicole Looper.