## The integral geometric Satake equivalence in mixed characteristic

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- by Jize Yu
- Represent. Theory
**26**(2022), 874-905 - DOI: https://doi.org/10.1090/ert/610
- Published electronically: August 18, 2022
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## Abstract:

Let $k$ be an algebraically closed field of characteristic $p$. Denote by $W(k)$ the ring of Witt vectors of $k$. Let $F$ denote a totally ramified finite extension of $W(k)[1/p]$ and $\mathcal {O}$ its ring of integers. For a connected reductive group scheme $G$ over $\mathcal {O}$, we study the category $\mathrm {P}_{L^+G}(Gr_G,\Lambda )$ of $L^+G$-equivariant perverse sheaves in $\Lambda$-coefficient on the Witt vector affine Grassmannian $Gr_G$ where $\Lambda =\mathbb {Z}_{\ell }$ and $\mathbb {F}_{\ell } \ (\ell \ne p)$, and prove that it is equivalent as a tensor category to the category of finitely generated $\Lambda$-representations of the Langlands dual group of $G$.## References

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## Bibliographic Information

**Jize Yu**- Affiliation: Department of Mathematics, Caltech, 1200 East California Boulevard, Pasadena, California 91125
- Address at time of publication: Room 228, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
- ORCID: 0000-0003-2887-743X
- Email: jzyu@math.cuhk.edu.hk
- Received by editor(s): August 24, 2020
- Received by editor(s) in revised form: January 28, 2022, and February 16, 2022
- Published electronically: August 18, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Represent. Theory
**26**(2022), 874-905 - MSC (2020): Primary 22E57; Secondary 14F06, 20G05, 14D24
- DOI: https://doi.org/10.1090/ert/610
- MathSciNet review: 4470196