Perverse sheaves on the semi-infinite flag variety and representations of the Frobenius kernel

2025/04/04 by Zabeth, Emilien
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.03341

Abstract

We study a category of Iwahori-equivariant modular perverse sheaves on some avatar of the semi-infinite flag variety, by adapting the work of Arkhipov-Bezrukavnikov-Braverman-Gaitsgory-Mirković. We then construct a functor between the latter category and the category of graded representations of the Frobenius kernel, and conjecture that this functor is an equivalence.

Related

• Modular perverse sheaves on flag varieties I: tilting and parity sheaves
• Perverse sheaves on affine flags and Langlands dual group
• Perverse sheaves and t-structures on the thin and thick affine flag varieties
• Modules over the small quantum group and semi-infinite flag manifold
• Kazhdan-Laumon Category O, Braverman-Kazhdan Schwartz space, and the semi-infinite flag variety