Abstract
We endow the set of lattices in $\mathbb{Q}_p^n$ with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake equivalence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
Citation
Xinwen Zhu. "Affine Grassmannians and the geometric Satake in mixed characteristic." Ann. of Math. (2) 185 (2) 403 - 492, March 2017. https://doi.org/10.4007/annals.2017.185.2.2
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