{"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/a-threefold-violating-a-local-to-global","title":"A threefold violating a local-to-global principle for rationality","arxiv_id":"2304.09306","date":"2023-04-18","proceeding":null,"authors":["Sarah Frei","Lena Ji"],"abstract":"In this note we construct an example of a smooth projective threefold that is irrational over $\\mathbb Q$ but is rational at all places. Our example is a complete intersection of two quadrics in $\\mathbb P^5$, and we show it has the desired rationality behavior by constructing an explicit element of order $4$ in the Tate--Shafarevich group of the Jacobian of an associated genus $2$ curve.","url_abs":"https://arxiv.org/abs/2304.09306v2","url_pdf":"https://arxiv.org/pdf/2304.09306v2.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":"a-threefold-violating-a-local-to-global","repo_url":"https://github.com/lena-ji/local-global-2quadrics","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}