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arXiv · 1002.3310

On Mordell-Weil groups of Jacobians over function fields

Douglas Ulmer
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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 $\C(t)$.

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Douglas Ulmer. 2011-02-18. On Mordell-Weil groups of Jacobians over function fields. https://arxiv.org/abs/1002.3310

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