A categorification of the colored Jones polynomial at a root of unity
You Qi, Louis-Hadrien Robert, Joshua Sussan, Emmanuel Wagner
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 $2p$th root of unity.