2025/04/25 by Huryn, Jake, Kedlaya, Kiran, Klevdal, Christian +1
#11G18 #14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2505.04492
In this article, we extend past results of the last two authors to include compatibility of canonical ℓ-adic local systems and canonical F-isocrystals on adjoint Shimura varieties in the superrigid regime. Our method relies on the crystallinity of canonical p-adic local systems due to Esnault--Groechenig as well as Margulis superrigidity and the crystalline-to-étale companion construction of Drinfeld and Kedlaya.