Geodesic
Geometrization of the Satake transform for mod p Hecke algebras
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e26

Voir la notice de l'article provenant de la source Cambridge University Press

We geometrize the mod p Satake isomorphism of Herzig and Henniart–Vignéras using Witt vector affine flag varieties for reductive groups in mixed characteristic. We deduce this as a special case of a formula, stated in terms of the geometry of generalized Mirković–Vilonen cycles, for the Satake transform of an arbitrary parahoric mod p Hecke algebra with respect to an arbitrary Levi subgroup. Moreover, we prove an explicit formula for the convolution product in an arbitrary parahoric mod p Hecke algebra. Our methods involve the constant term functors inspired from the geometric Langlands program, and we also treat the case of reductive groups in equal characteristic. We expect this to be a first step toward a geometrization of a mod p Local Langlands Correspondence. 
Cass, Robert; Xu, Yujie. Geometrization of the Satake transform for mod p Hecke algebras. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e26. doi: 10.1017/fms.2024.130
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     title = {Geometrization of the {Satake} transform for mod p {Hecke} algebras},
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