S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas

2021/10/20 by Zhiyou Wu, Wu, Zhiyou
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.10350

openalex publication_date 2021/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the S=T conjecture proposed by Xiao--Zhu in \cite2017arXiv170705700X, making use of Scholze's theory of diamonds and v-stacks and Fargues--Scholze's geometric Satake equivalence. Following \cite2018arXiv180205299X, we deduce the Eichler--Shimura relation for Shimura varieties of Hodge type.

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