The Zilber-Pink conjecture for abelian varieties over number fields

Claims that for any abelian variety over a number field, every irreducible subvariety has only finitely many maximal atypical subvarieties inside its smallest containing torsion coset, via a non-density theorem for $X\cap A^{[\dim X+1]}$ for $X$ in no proper torsion coset. A corollary gives the abelian algebraic-point case of Pink's Conjecture 5.2 for finite-rank translates. It does NOT treat semiabelian varieties, abelian varieties over $\mathbb C$ not defined over $\bar{\mathbb Q}$, or Shimura varieties, and gives no effective or uniform bound.

Claims that for any abelian variety over a number field, every irreducible subvariety has only finitely many maximal atypical subvarieties inside its smallest containing torsion coset, via a non-density theorem for $X\cap A^{[\dim X+1]}$ for $X$ in no proper torsion coset. A corollary gives the abelian algebraic-point case of Pink's Conjecture 5.2 for finite-rank translates. It does NOT treat semiabelian varieties, abelian varieties over $\mathbb C$ not defined over $\bar{\mathbb Q}$, or Shimura varieties, and gives no effective or uniform bound.