{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/rational-torsion-points-on-abelian-surfaces","title":"Rational torsion points on abelian surfaces with quaternionic multiplication","arxiv_id":"2308.15193","date":"2023-08-29","proceeding":null,"authors":["Jef Laga","Ciaran Schembri","Ari Shnidman","John Voight"],"abstract":"Let $A$ be an abelian surface over $\\mathbb{Q}$ whose geometric endomorphism ring is a maximal order in a non-split quaternion algebra. Inspired by Mazur's theorem for elliptic curves, we show that the torsion subgroup of $A(\\mathbb{Q})$ is $12$-torsion and has order at most $18$. Under the additional assumption that $A$ is of $\\mathrm{GL}_2$-type, we give a complete classification of the possible torsion subgroups of $A(\\mathbb{Q})$.","url_abs":"https://arxiv.org/abs/2308.15193v1","url_pdf":"https://arxiv.org/pdf/2308.15193v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"rational-torsion-points-on-abelian-surfaces","repo_url":"https://github.com/ciaran-schembri/qm-mazur","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}