Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 016-04. Elliptic squares and Zilber–Pink for curves in A2
Manuscript map · lines 2835–2844
OpenAI@2026-10-07#rem:oai-p-016-04
Authors: OpenAI. Family 016.
Title: Elliptic squares and Zilber–Pink for curves in A2.
Abstract: We prove that every Hodge-generic algebraic curve in ${}mathcal A_2$ over ${}overline{{}mathbb Q}$ contains only finitely many points whose abelian surface is isogenous to the square of an elliptic curve without complex multiplication (CM). Combining this result with the companion $E{}times{}mathrm{CM}$ and quaternionic-division finiteness theorems, we prove the curve case of Zilber–Pink in ${}mathcal A_2$ over ${}overline{{}mathbb Q}$, without a boundary hypothesis.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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