Zilber-Pink for Hodge-generic curves in the Siegel modular threefold A_2

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

Companion: The E x CM component of Zilber-Pink for curves in A2 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

Claims the full curve case of Zilber-Pink in $\mathcal A_2$ over $\bar{\mathbb Q}$: a Hodge-generic algebraic curve contains only finitely many points whose abelian surface is isogenous to a product with a CM factor, to the square of a non-CM elliptic curve, or has quaternionic-division endomorphism algebra, besides finitely many special points. Previous unconditional results needed the curve to meet the Baily-Borel boundary or to have multiplicative degeneration. It does NOT treat higher-dimensional subvarieties of $\mathcal A_2$, $\mathcal A_g$ for $g\ge3$, or curves not defined over $\bar{\mathbb Q}$. parent of this event

VibeMathed record: Zilber-Pink for Hodge-generic curves in the Siegel modular threefold A_2 evidence for this event

Companion: Quaternionic division points on curves in the Siegel threefold evidence for this event

Zilber-Pink for Hodge-generic curves in the Siegel modular threefold A_2 parent of this event