On the classification of simple amenable $C\ast$-algebras with finite decomposition rank, II

We prove that every unital stably finite simple amenable $C^{\ast }$-algebra $A$ with finite nuclear dimension and with UCT such that every trace is quasi-diagonal has the property that $A\otimes Q$ has generalized tracial rank at most one, where $Q$ is the universal UHF-algebra. Consequently, $A$ is classifiable in the sense of Elliott.