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

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar