Relation between the two geometric Satake equivalence via nearby cycle

Abstract

Fargues and Scholze proved the geometric Satake equivalence over the Fargues--Fontaine curve. On the other hand, Zhu proved the geometric Satake equivalence using a Witt vector affine Grassmannian. In this paper, we explain the relation between the two version of the geometric Satake equivalence via nearby cycle.

20 pages, changed the arguments in section 3.1 and some minor errors