Abelian Varieties over Number Fields of Infinite Degree:

Suppose A is an abelian variety defined over a finite number field K.
It is well known that A(K) is a finitely generated abelian group.
Suppose L/K is a, possibly infinite, algebraic extension of K. What
can be said about the structure of A(L)? The talk will survey the
known results. It will also exposit a contribution of M. Rosen and S.
Wong in the case where A is the Jacobian of a cyclic cover of P^1.