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arXiv:1002.3310 [math.NT]AbstractReferencesReviewsResources

On Mordell-Weil groups of Jacobians over function fields

Douglas Ulmer

Published 2010-02-17, updated 2011-02-18Version 3

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 $\C(t)$.

Comments: 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
Categories: math.NT, math.AG
Subjects: 14G05, 11G40
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