{"id":"openai-math/Elliptic-Squares-and-Zilber-Pink-for-Curves-in-A2","pdf":"https://github.com/openai/math/blob/main/preprints/Elliptic-Squares-and-Zilber-Pink-for-Curves-in-A2-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Elliptic-Squares-and-Zilber-Pink-for-Curves-in-A2-September-24-2026","tags":["arithmetic-geometry","abelian-varieties","zilber-pink"],"score":0,"title":"Elliptic squares and Zilber–Pink for curves in A2","domain":"Number theory","family":"016","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Zilber–Pink in abelian varieties and the Siegel threefold"}