The Arkhipov-Bezrukavnikov equivalence over the integers

Abstract: In joint work with Gurbir Dhillon, we prove a universal monodromic extension of Bezrukavnikov’s two realizations of the affine Hecke category over the integers. I will discuss some ingredients that go into to the proof of the Arkhipov-Bezrukavnikov equivalence in this setting. These include analysis of multi-graded rings, deformation between characteristic zero and positive characteristic, and the tilting property of Whittaker averaged central sheaves. The proof of the latter is based on ideas of Faergeman-Raskin and Bezrukavnikov-Morton-Ferguson.