Constant term functors with $\mathbb{F}_p$-coefficients

Robert Cass; Cédric Pépin

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arXiv · 2107.00714

Constant term functors with $\mathbb{F}_p$-coefficients

Robert Cass·Cédric Pépin

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Abstract

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.

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BibTeX RIS

Robert Cass, Cédric Pépin. 2021-07-01. Constant term functors with $\mathbb{F}_p$-coefficients. https://arxiv.org/abs/2107.00714

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