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Quantum supergroups VI. Roots of $1$

A quantum covering group is an algebra with parameters $q$ and $π$ subject to $π^2=1$ and it admits an integral form; it specializes to the usual quantum group at $π=1$ and to a quantum supergroup of anisotropic type at $π=-1$. In this paper we establish the Frobenius-Lusztig homomorphism and Lusztig-Steinberg tensor product theorem in the setting of quantum covering groups at roots of 1. The specialization of these constructions at $π=1$ recovers Lusztig's constructions for quantum groups at roots of 1.