On Mordell-Weil groups of Jacobians over function fields

Abstract

We study the arithmetic of abelian varieties over $K=k(t)$ where $k$ is an arbitrary field. The main result relates Mordell-Weil groups of certain Jacobians over $K$ to homomorphisms of other Jacobians over $k$. Our methods also yield completely explicit points on elliptic curves with unbounded rank over $\Fpbar(t)$ and a new construction of elliptic curves with moderately high rank over $\C(t)$.

v1: 25 pages; v2=v1, ignore; v3: Corrects rank formula when the covers C_d or D_d are reducible and includes other minor improvements and simplifications