Two monoidal structures on Satake category in mixed characteristic
Abstract
Fargues and Scholze proved the geometric Satake equivalence over the Fargues–Fontaine curve. This can be transferred to the geometric Satake equivalence concerning a Witt vector affine Grassmannian via a nearby cycle. On the other hand, Zhu proved the geometric Satake equivalence concerning a Witt vector affine Grassmannian. In this paper, we explain the coincidence of these two geometric Satake equivalences, including the coincidence of the two symmetric monoidal structures on the Satake category.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Advanced Algebra and Geometry
Publication details
- Journal / source
- Journal de Théorie des Nombres de Bordeaux
- Volume
- 38
- Issue
- 1
- Pages
- 1–25
- Publication date
- 24 April 2026
- Language
- EN