S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912385626800128 |
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| author | Wu, Zhiyou |
| author_facet | Wu, Zhiyou |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10350 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas Wu, Zhiyou Number Theory Algebraic Geometry 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. |
| title | S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2110.10350 |