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On the rank of abelian varieties over function fields

Amilcar Pacheco
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Abstract

Let $\cac$ be a smooth projective curve defined over a number field $k$, $A/k(\cac)$ an abelian variety and $(τ,B)$ the $k(\cac)/k$-trace of $A$. We estimate how the rank of $A(k(\cac))/τB(k)$ varies when we take a finite cover $π:\cac'\to\cac$ defined over $k$ geometrically abelian.

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Amilcar Pacheco. 2005-09-07. On the rank of abelian varieties over function fields. https://arxiv.org/abs/math/0404384

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