The isolated-singularity tensor product conjecture for maximal Cohen–Macaulay modules

Let $R$ be a local complete intersection domain, and let $M,N\in\operatorname{mod} R$. Assume that $R$ is an isolated singularity. Tensor-product maximal Cohen–Macaulay conjecture. If $M\otimes_R N$ is maximal Cohen–Macaulay, then $M$ or $N$ is maximal Cohen–Macaulay.

This conjecture extends the corresponding question beyond codimension at most one, where it is known. It remains open even under the isolated-singularity and maximal Cohen–Macaulay hypotheses.