{"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/on-abelian-varieties-whose-torsion-is-not","title":"On abelian varieties whose torsion is not self-dual","arxiv_id":"2309.00531","date":"2023-09-01","proceeding":null,"authors":["Sarah Frei","Katrina Honigs","John Voight"],"abstract":"We construct infinitely many abelian surfaces A defined over the rational numbers such that, for a prime ell <= 7, the ell-torsion subgroup of A is not isomorphic as a Galois module to the ell-torsion subgroup of its dual. We do this by explicitly analyzing the action of the Galois group on the ell-adic Tate module and its reduction modulo ell.","url_abs":"https://arxiv.org/abs/2309.00531v3","url_pdf":"https://arxiv.org/pdf/2309.00531v3.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":"on-abelian-varieties-whose-torsion-is-not","repo_url":"https://github.com/sjfrei/fhv-abeliansurfaces","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}