Vasconcelos's flatness criterion for algebras

Let $R$ be a regular ring of dimension $n>0$, and let $A$ be an $R$-algebra essentially of finite type.

Vasconcelos's conjecture. $A$ is $R$-flat if and only if its $n$-fold tensor power

$$A^{\otimes^n_R}$$

is torsion-free over $R$.

This conjecture extends Auslander's freeness criterion from finite modules to algebras that are essentially of finite type over a regular ring. The source presents it as a conjecture of Vasconcelos; no resolution is given in the supplied text.