2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96464Let $\cac$ 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.final version, to appear Manuscripta MathematicaNumber TheoryAlgebraic Geometrytext