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

Zhiyou Wu

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arXiv · 2110.10350

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

Zhiyou Wu

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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.

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Zhiyou Wu. 2021-10-20. S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas. https://arxiv.org/abs/2110.10350

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