Modular Koszul duality for Soergel bimodules

Abstract

We generalize the modular Koszul duality of Achar–Riche [4] to the setting of Soergel bimodules associated to any finite Coxeter system. The key new tools are a functorial monodromy action and wall-crossing functors in the mixed modular derived category of [4]. In characteristic 0, this duality together with Soergel's conjecture (proved by Elias–Williamson [14]) imply that our Soergel-theoretic graded category O is Koszul self-dual, generalizing the result of Beilinson–Ginzburg–Soergel [25,8].