Gaitsgory's central functor and the Arkhipov-Bezrukavnikov equivalence for p-adic groups

In 2002, Arkhipov and Bezrukavnikov established an equivalence between the Iwahori-equivariant derived category of constructible \ell-adic sheaves and the Langlands dual group equivariant derived category of coherent sheaves on the Langlands dual Springer resolution for a connected reductive group over. In this talk, we discuss this equivalence for p-adic groups by constructing a mixed-characteristic Gaitsgory's central functor. This is a joint work with J. Anschütz, J. Lourenco, and Z. Wu.