Strict-henselization finiteness conjecture for rank-one maximal Cohen–Macaulay modules

Let $R$ be a local normal domain, and let $R^{sh}$ denote its strict henselization. The group $\operatorname{Cl}(R^{sh})$ is the divisor class group of the strict henselization. Strict-henselization finiteness conjecture. If $\operatorname{Cl}(R^{sh})$ is finitely generated, then there exist only finitely many maximal Cohen–Macaulay modules of rank one up to isomorphism. This is a proposed refinement of the finiteness question for Cohen–Macaulay ideals; the supplied text gives no resolution status.