{"id":"openai-math/Quaternionic-Division-Points-on-Curves-in-the-Siegel-Threefold","pdf":"https://github.com/openai/math/blob/main/preprints/Quaternionic-Division-Points-on-Curves-in-the-Siegel-Threefold-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Quaternionic-Division-Points-on-Curves-in-the-Siegel-Threefold-September-24-2026","tags":["arithmetic-geometry","shimura-varieties","zilber-pink","abelian-varieties"],"score":0,"title":"Quaternionic division points on curves in the Siegel threefold","domain":"Number theory","family":"016","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove the quaternionic-division component of Zilber–Pink for curves in $`\\mathcal A_2`$ over $`\\overline{\\mathbb Q}`$. A Hodge-generic algebraic curve contains only finitely many points whose full geometric rational endomorphism algebra is an indefinite quaternion division algebra over ℚ. No boundary or reduction hypothesis is required.","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"}