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

Zhiyou Wu

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

Number Theory 2025-05-22 v3 Algebraic Geometry

Authors: Zhiyou Wu

Abstract

We prove the $S=T$ conjecture proposed by Xiao--Zhu in \cite{2017arXiv170705700X}, making use of Scholze's theory of diamonds and v-stacks and Fargues--Scholze's geometric Satake equivalence. Following \cite{2018arXiv180205299X}, we deduce the Eichler--Shimura relation for Shimura varieties of Hodge type.

Keywords

s=t conjecture shimura varieties p-adic shtukas diamonds v-stacks geometric satake equivalence eichler-shimura relation

Cite

@article{arxiv.2110.10350,
  title  = {S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas},
  author = {Zhiyou Wu},
  journal= {arXiv preprint arXiv:2110.10350},
  year   = {2025}
}

Comments

Exposition improved. Minor corrections following the suggestions of the referees

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