The Zilber-Pink conjecture for abelian varieties over number fields

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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. parent of this event

The Zilber-Pink conjecture for abelian varieties over number fields parent of this event

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Family companion: Elliptic squares and Zilber-Pink for curves in A2 (separate entry) evidence for this event

Pink (2005), A common generalization of the conjectures of Andre-Oort, Manin-Mumford, and Mordell-Lang evidence for this event

The Zilber-Pink conjecture for abelian varieties over number fields evidence for this event

VibeMathed record: The Zilber-Pink conjecture for abelian varieties over number fields evidence for this event

Zilber (2002), Exponential sums equations and the Schanuel conjecture evidence for this event