Geodesic
Constant term functors with $\mathbb{F}_{p}$-coefficients
Documenta mathematica, Tome 29 (2024) no. 2, pp. 343-397

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We study the constant term functor for Fp​-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 Fp​-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.
DOI : 10.4171/dm/955
Classification : 14D24, 14F10, 14M15, 20C08
Mots-clés : constant terms, perverse mod p sheaves, affine Grassmannian, Satake transform 
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     title = {Constant term functors with $\mathbb{F}_{p}$-coefficients},
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     year = {2024},
     doi = {10.4171/dm/955},
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Robert Cass; Cédric Pépin. Constant term functors with $\mathbb{F}_{p}$-coefficients. Documenta mathematica, Tome 29 (2024) no. 2, pp. 343-397. doi: 10.4171/dm/955

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