Papers › Dwork Motives, Monodromy and Potential Automorphy
Dwork Motives, Monodromy and Potential Automorphy
Lambert A'Campo
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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 SLₙ. Secondly, they realise many different unipotent operators as the monodromy operator at t = ∞. Thirdly, all their Hodge numbers are ≤1. This has consequences for Galois representations. Namely, if a nilpotent operator N appears as the monodromy at t = ∞ in one of our families, we can construct potentially automorphic representations with ℓ-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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections