4 papers · 1 filter
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…
A Note on the Specialization Theorem for Families of Abelian Varieties
Rania Wazir
In this note, we apply Moriwaki's arithmetic height functions to obtain an analogue of Silverman's Specialization Theorem for families of Abelian varieties over , where is a…
A Local-global Summation Formula for Abelian Varieties
Rania Wazir
Let be a field finitely generated over ${\Q}$, and an Abelian variety defined over . Then by the Mordell-Weil Theorem, the set of rational points is a finitely-ge…
Arithmetic on Elliptic Threefolds
Rania Wazir
In a recent paper, Rosen and Silverman showed that Tate's conjecture on the order of vanishing of L(E,s) implies Nagao's formula, which gives the rank of an elliptic surface in ter…