{"id":"openai-math/The-E-times-CM-Component-of-Zilber-Pink-for-Curves-in-A2","pdf":"https://github.com/openai/math/blob/main/preprints/The-E-times-CM-Component-of-Zilber-Pink-for-Curves-in-A2-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-E-times-CM-Component-of-Zilber-Pink-for-Curves-in-A2-September-24-2026","tags":["algebraic-geometry","zilber-pink","abelian-varieties","complex-multiplication"],"score":0,"title":"The E×CM component of 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 the $`E\\times\\mathrm{CM}`$ component of Zilber–Pink for Hodge-generic algebraic curves in $`\\mathcal A_2`$ over $`\\overline{\\mathbb Q}`$. Each such curve contains only finitely many points whose abelian surface is isogenous to a product of elliptic curves with at least one factor having complex multiplication.","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"}