The prismatic realization functor for Shimura varieties of abelian type

2023/10/12 by Naoki Imai, Imai, Naoki, Hiroki Kato +3 · 1 citation
Mathematics · #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.2310.08472

openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the integral canonical model \mathscrS_K^p of a Shimura variety Sh_K0K^p(G,X) of abelian type at hyperspecial level K₀=G(ℤ_p), we construct a prismatic F-gauge model for the `universal' G(ℤ_p)-local system on Sh_K0K^p(G,X). We use this to obtain several new results about the p-adic geometry of Shimura varieties, notably an abelian-type analogue of the Serre--Tate deformation theorem (realizing an expectation of Drinfeld in the abelian-type case) and a prismatic characterization of these models at individual level.

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• Singularities in the Ekedahl--Oort stratification

Related

• Canonical Integral Models of Shimura Varieties of Abelian Type
• Filtered F-crystals on Shimura varieties of abelian type
• Generalized Serre--Tate Ordinary Theory
• Deformation theory for prismatic G-displays
• G-μ-displays and local shtuka