On the variation of the rank of Jacobian varieties on unramified abelian towers over number fields

Mathematics – Number Theory

Scientific paper

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11 pages, revised version

Scientific paper

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 $k$.

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