Affine Grassmannians and the geometric Satake in mixed characteristic
  We endow the set of lattices in Q_p^n with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake correspondence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces. 
Xinwen Zhu
math.AG math.NT math.RT