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math.NT2004
On the rank of abelian varieties over function fields
Amilcar Pacheco
Let $\cac$ be a smooth projective curve defined over a number field , $A/k(\cac)$ an abelian variety and the $k(\cac)/k$-trace of . We estimate how the rank of $A(k(\…
math.NT2003★ 1 cited
On the variation of the rank of Jacobian varieties on unramified abelian towers over number fields
Amilcar Pacheco
Let be a smooth projective curve defined over a number field , a smooth projective curve of positive genus, the Jacobian variety of and the $k(C)/…
math.NT2003
Fibrations et conjecture de Tate
Marc Hindry, Amilcar Pacheco, Rania Wazir
We describe the behaviour of the rank of the Mordell-Weil group of the Picard variety of the generic fibre of a fibration in terms of local contributions given by averaging traces…