The finite–discrete–tame–wild trichotomy conjecture for Cohen–Macaulay modules

Let $(A,\mathfrak{m})$ be a local Cohen–Macaulay ring of Krull dimension two. The finite–discrete–tame–wild trichotomy conjecture. The representation type of the category of Cohen–Macaulay $A$-modules $\operatorname{CM}(A)$ is one of finite, discrete, tame, or wild. A positive solution is known for reduced curve singularities, while the two-dimensional case remains open.