{"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/geometric-decomposition-of-abelian-varieties","title":"Geometric decomposition of abelian varieties of order 1","arxiv_id":"2109.03986","date":"2021-09-09","proceeding":null,"authors":["Toren D'Nelly-Warady","Kiran S. Kedlaya"],"abstract":"Since the 1970s, the complete classification (up to isogeny) of abelian varieties over finite fields with trivial group of rational points has been known from results of Madan--Pal and Robinson; with two exceptions these are all defined over $\\mathbb{F}_2$. We determine the decomposition of these varieties into simple factors over an algebraic closure of $\\mathbb{F}_2$; this requires solving a polynomial equation in three roots of unity.","url_abs":"https://arxiv.org/abs/2109.03986v2","url_pdf":"https://arxiv.org/pdf/2109.03986v2.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":"geometric-decomposition-of-abelian-varieties","repo_url":"https://github.com/mwarady22/geometric-decomposition-of-abelian-varieties-of-order-1","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}