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

Explore recent advances in the uniform boundedness conjecture for abelian varieties over function fields in this mathematical lecture from the Joint IAS/PU Number Theory seminar. Delve into the conjecture that predicts the existence of a constant N, dependent only on the genus g and function field K of a smooth projective curve over complex numbers, such that any K-rational torsion point of a g-dimensional abelian variety A over K has order at most N. Examine new progress made under the assumption that A has semistable reduction over K, presented through collaborative research findings. Learn about the theoretical framework connecting algebraic geometry, number theory, and the behavior of torsion points in abelian varieties defined over function fields of curves.