Abelian fibrations and SYZ mirror conjecture

SYZ mirror conjecture predicts that a Calabi-Yau manifold $X$ consists of a family of tori which are dual to a family of special lagrangian tori on the mirror dual manifold $\widehat{X}$. Here we consider a fibration of polarized abelian varieties and we construct a dual one. Moreover we prove that they are equivalent at the level of derived categories.