%0 Journal Article %T On the variation of the rank of Jacobian varieties on unramified abelian towers over number fields %A Amilcar Pacheco %J Mathematics %D 2003 %I arXiv %X Let $C$ be a smooth projective curve defined over a number field $k$, $X/k(C)$ a smooth projective curve of positive genus, $J_X$ the Jacobian variety of $X$ and $(\tau,B)$ the $k(C)/k$-trace of $J_X$. We estimate how the rank of $J_X(k(C))/\tau B(k)$ varies when we take an unramified abelian cover $\pi:C'\to C$ defined over $k$. %U http://arxiv.org/abs/math/0310123v2