Modular affine Hecke category and regular unipotent centralizer

Abstract: In this paper we provide, under some mild explicit assumptions, a geometric description of the category of representations of the centralizer of a regular unipotent element in a reductive algebraic group in terms of perverse sheaves on the Langlands dual affine flag variety. This equivalence is suggested and motivated by the "geometric Langlands" philosophy, and is used in later work to construct equivalences of categories relating various geometric incarnations of the affine Hecke algebra of the given reductive group.