Higher-dimensional Huneke–Wiegand tensor product conjecture

Let $R$ be a Cohen–Macaulay ring of dimension at least one, and let $M$ be a finitely generated $R$-module. Set $M^* = \operatorname{Hom}_R(M,R)$. A module is reflexive when the canonical map to its double dual is an isomorphism.

Higher-dimensional Huneke–Wiegand conjecture. If $M\otimes_R M^*$ is reflexive, then $M$ is free.

This is suggested by examples showing that the one-dimensional tensor-product condition can fail in higher dimensions without stronger depth assumptions. The source presents this as a proposed higher-dimensional version; its general status is not resolved there.