{"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/explicit-lower-bounds-on-the-conductors-of","title":"Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields","arxiv_id":"2410.12922","date":"2024-10-16","proceeding":null,"authors":["Tchamitchian Pierre"],"abstract":"Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields. Moreover, we obtain bounds for the conductor of elliptic curves and abelian varieties over $\\mathbb{Q}$ with specified bad reduction and over number fields. As an application, for specific fields, we prove the non-existence of abelian varieties with everywhere good reduction.","url_abs":"https://arxiv.org/abs/2410.12922v1","url_pdf":"https://arxiv.org/pdf/2410.12922v1.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":"explicit-lower-bounds-on-the-conductors-of","repo_url":"https://github.com/pierretchamitchian/conductor-of-abelian-varieties-over-number-fields","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}