# Modular Koszul duality for Soergel bimodules

## TL;DR

This paper extends modular Koszul duality to Soergel bimodules for any finite Coxeter system, introducing new functorial tools and showing that certain categories are Koszul self-dual in characteristic 0.

## Contribution

It generalizes modular Koszul duality to a broader setting of Soergel bimodules and introduces functorial monodromy and wall-crossing functors as new tools.

## Key findings

- Duality implies graded category $\ ext{O}$ is Koszul self-dual in characteristic 0
- Generalizes previous duality results to all finite Coxeter systems
- Uses new functorial monodromy and wall-crossing functors

## Abstract

We generalize the modular Koszul duality of Achar-Riche 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. In characteristic 0, this duality together with Soergel's conjecture (proved by Elias-Williamson) imply that our Soergel-theoretic graded category $\mathcal{O}$ is Koszul self-dual, generalizing the result of Beilinson-Ginzburg-Soergel.