2024/07/23 by Lambert A'Campo, A'Campo, Lambert
Business, Management and Accounting · #11R39 #14D05 #Algebraic Geometry (math.AG) #Business Strategy and Innovation #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2407.16481
openalex publication_date 2024/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.