On Mordell-Weil groups of Jacobians over function fields

Details On Mordell-Weil groups of Jacobians over function fields On Mordell-Weil groups of Jacobians over function fields

2010-02-17

arxiv.org/abs/1002.3310v3

Mathematics

Number Theory

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

Scientific paper

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 $\C(t)$.

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