Categoricity of Shimura Varieties

2018/03/18 by Sebastian Eterović, Eterović, Sebastian
Mathematics · #03C98 11G18 14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1803.06700

openalex publication_date 2018/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from Galois representations attached the points of a Shimura variety. We end by showing that the existing literature is enough to prove categoricity of A₂ and A₃.

Related

• Local models of Shimura varieties, I. Geometry and combinatorics
• Arithmetic models for Shimura varieties
• Shimura varieties
• Geometric Satake, categorical traces, and arithmetic of Shimura varieties
• Complex Multiplication and Shimura Stacks