The integral coefficient geometric Satake equivalence in mixed characteristic

The geometric Satake equivalence establishes a link between two categories: the category of spherical perverse sheaves on the affine Grassmannian and the category of representations of the Langlands dual group. It has found many important applications in the study of the geometric Langlands program and number theory. Lusztig, Ginzburg, and Mirkovic-Vilonen pioneered the study of this equivalence in equal characteristic. Later, Zhu established the equivalence in the mixed characteristic setting for ℚ¯ℓ-coefficient perverse sheaves. Peter Scholze announced a result for the general coefficient perverse sheaves in mixed characteristic using the beautiful theory of diamonds. In this talk, I will discuss the integral coefficient geometric Satake equivalence in the mixed characteristic setting using a different approach.