{"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/local-isomorphism-classes-of-fractional","title":"Local isomorphism classes of fractional ideals of orders in étale algebras","arxiv_id":"2311.18571","date":"2023-11-30","proceeding":null,"authors":["Stefano Marseglia"],"abstract":"We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in \\'etale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods.","url_abs":"https://arxiv.org/abs/2311.18571v2","url_pdf":"https://arxiv.org/pdf/2311.18571v2.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":"local-isomorphism-classes-of-fractional","repo_url":"https://github.com/stmar89/alget","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}