On the rank of abelian varieties over function fields

Amilcar Pacheco

On the rank of abelian varieties over function fields

Number Theory 2007-05-23 v3 Algebraic Geometry

Authors: Amilcar Pacheco

Abstract

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.

Keywords

abelian varieties toric varieties hyperelliptic curves

Cite

@article{arxiv.math/0404384,
  title  = {On the rank of abelian varieties over function fields},
  author = {Amilcar Pacheco},
  journal= {arXiv preprint arXiv:math/0404384},
  year   = {2007}
}

Comments

final version, to appear Manuscripta Mathematica

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