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arXiv · 1703.01576

Modular Koszul duality for Soergel bimodules

Shotaro Makisumi
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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.

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BibTeXRIS

Shotaro Makisumi. 2017-03-05. Modular Koszul duality for Soergel bimodules. https://arxiv.org/abs/1703.01576

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