A categorification of the colored Jones polynomial at a root of unity

There is a p-differential on the triply-graded Khovanov–Rozansky homology of knots and links over a field of positive characteristic p that gives rise to an invariant in the homotopy category finite-dimensional p-complexes. A differential on triply-graded homology discovered by Cautis is compatible with the p-differential structure. As a consequence we get a categorification of the colored Jones polynomial evaluated at a 2pth root of unity.

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