Constant term functors with -coefficients

  • Robert Cass

    University of Michigan, Ann Arbor, USA
  • Cédric Pépin

    Institut Galilée, Université Sorbonne Paris Nord, Villetaneuse, France
Constant term functors with $\mathbb{F}_{p}$-coefficients cover
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We study the constant term functor for -sheaves on the affine Grassmannian in characteristic with respect to a Levi subgroup. Our main result is that the constant term functor induces a tensor functor between categories of equivariant perverse -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 Satake transform and the structure of the space of mod Satake parameters.

Cite this article

Robert Cass, Cédric Pépin, Constant term functors with -coefficients. DM 29 (2024), no. 2, pp. 343–397

DOI 10.4171/DM/955