Compatibility of canonical ℓ-adic local systems on Shimura varieties, II

2025/04/01 by Stefan Patrikis, Patrikis, Stefan · 1 citation
Mathematics · #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.00305

openalex publication_date 2025/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (G, X) be a Shimura datum. In previous work with Christian Klevdal, we showed that the canonical G(ℚ_ℓ)-valued local systems on Shimura varieties for G form compatible systems after projection to the adjoint group of G. In this note, we strengthen this result to prove compatibility for the G(ℚ_ℓ)-local systems themselves. We also include the crystalline compatibility, extending the adjoint case established in our joint work Jake Huryn, Kiran Kedlaya, and Christian Klevdal.

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