On the rank of abelian varieties over function fields

Details On the rank of abelian varieties over function fields On the rank of abelian varieties over function fields

2004-04-21

arxiv.org/abs/math/0404384v3

Manuscripta Mathematica 118( 2005), 361-381

Mathematics

Number Theory

final version, to appear Manuscripta Mathematica

Scientific paper

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

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