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Peer-reviewedCC BY 4.0Forum of Mathematics, Sigma

S = T S=T upper S equals upper T for Shimura varieties and moduli spaces of p -adic shtukas

  • Zhiyou Wu1
  1. 1Morningside Center for Mathematics
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Abstract

We prove the S = T S=T upper S equals upper T conjecture proposed by Xiao–Zhu in [XZ17], making use of Scholze’s theory of diamonds and v-stacks and Fargues–Scholze’s geometric Satake equivalence. Following [XZ18], we deduce the Eichler–Shimura relation for Shimura varieties of Hodge type.

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Cite

BibTeXRIS
BibTeX
@article{wu2026upper,
  title = {{S = T $S=T$ upper S equals upper T for Shimura varieties and moduli spaces of p -adic shtukas}},
  author = {Zhiyou Wu},
  journal = {Forum of Mathematics, Sigma},
  year = {2026},
  month = nov,
  doi = {10.1017/fms.2026.10271},
  url = {https://www.cambridge.org/core/product/identifier/S2050509426102710/type/journal_article},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - S = T S=T upper S equals upper T for Shimura varieties and moduli spaces of p -adic shtukas
AU  - Zhiyou Wu
PY  - 2026
DA  - 2026/11/04
JO  - Forum of Mathematics, Sigma
DO  - 10.1017/fms.2026.10271
UR  - https://www.cambridge.org/core/product/identifier/S2050509426102710/type/journal_article
AB  - We prove the S = T S=T upper S equals upper T conjecture proposed by Xiao–Zhu in [XZ17], making use of Scholze’s theory of diamonds and v-stacks and Fargues–Scholze’s geometric Satake equivalence. Following [XZ18], we deduce the Eichler–Shimura relation for Shimura varieties of Hodge type.
SN  - 2050-5094
ER  -