{"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/dwork-motives-monodromy-and-potential","title":"Dwork Motives, Monodromy and Potential Automorphy","arxiv_id":"2407.16481","date":"2024-07-23","proceeding":null,"authors":["Lambert A'Campo"],"abstract":"In this paper we study certain families of motives, which arise as direct summands of the cohomology of the Dwork family. We computationally find examples of interesting families with the following three properties. Firstly, their geometric monodromy group is Zariski dense in $\\operatorname{SL}_n$. Secondly, they realise many different unipotent operators as the monodromy operator at $t = \\infty$. Thirdly, all their Hodge numbers are $\\leq 1$. This has consequences for Galois representations. Namely, if a nilpotent operator $N$ appears as the monodromy at $t = \\infty$ in one of our families, we can construct potentially automorphic representations with $\\ell$-adic monodromy given by $N$ at a fixed prime $p$. As another application, we obtain a new proof of some cases of the recent local-global compatibility theorem of Matsumoto.","url_abs":"https://arxiv.org/abs/2407.16481v1","url_pdf":"https://arxiv.org/pdf/2407.16481v1.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":"dwork-motives-monodromy-and-potential","repo_url":"https://github.com/LAC1213/dworkmotives","is_official":1,"mentioned_in_paper":0,"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}