Affine Grassmannians and the geometric Satake in mixed characteristic


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.


Xinwen Zhu

California Institute of Technology, Pasadena, CA