{"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-a-fiber-conjecture-of-wan","title":"On a Fiber Conjecture of Wan","arxiv_id":"2311.14819","date":"2023-11-24","proceeding":null,"authors":["Matthew Schmidt"],"abstract":"For a prime $p$ and $p$-power $q$, let $f(x)\\in\\mathbb{F}_q[x]$ with $\\textrm{deg}\\ f$ coprime to $p$. As $\\lambda$ varies in $\\overline{\\mathbb{F}_p^\\times}$, Wan has conjectured that the $p$-adic Newton polygon of the corresponding Artin-Schreier curve given by $\\lambda f$ is constant. That is, \\[ \\textrm{NP}(f) = \\textrm{NP}(\\lambda f). \\] In this paper, we prove this conjecture when $\\lambda\\in\\mathbb{F}_p^\\times$ and provide a detailed counterexample showing it is false in general.","url_abs":"https://arxiv.org/abs/2311.14819v2","url_pdf":"https://arxiv.org/pdf/2311.14819v2.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-a-fiber-conjecture-of-wan","repo_url":"https://github.com/exponentialsums/fiber","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}