Constant term functors with \(\mathbb{F}_p\)-coefficients (Q6200602)

Summary: We study the constant term functor for \(\mathbb{F}_p\)-sheaves on the affine Grassmannian in characteristic \(p\) with respect to a Levi subgroup. Our main result is that the constant term functor induces a tensor functor between categories of equivariant perverse \(\mathbb{F}_p\)-sheaves. We apply this fact to get information about the Tannakian monoids of the corresponding categories of perverse sheaves. As a byproduct we also obtain geometric proofs of several results due to Herzig on the mod \(p\) Satake transform and the structure of the space of mod \(p\) Satake parameters.