S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas
Abstract
We prove the S=T conjecture proposed by Xiao--Zhu in 2017arXiv170705700X, making use of Scholze's theory of diamonds and v-stacks and Fargues--Scholze's geometric Satake equivalence. Following 2018arXiv180205299X, we deduce the Eichler--Shimura relation for Shimura varieties of Hodge type.
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