The Zilber-Pink conjecture for abelian varieties over arbitrary algebraically closed fields of characteristic 0 is reduced to the conjecture over the algebraic numbers, and is proved for subvarieties of defect at most 1 over the algebraic numbers.
Conrad, Chow's K/k -image and K/k -trace, and the L ang- N \' e ron theorem , Enseign
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On the Zilber-Pink conjecture for complex abelian varieties
The Zilber-Pink conjecture for abelian varieties over arbitrary algebraically closed fields of characteristic 0 is reduced to the conjecture over the algebraic numbers, and is proved for subvarieties of defect at most 1 over the algebraic numbers.