Krull--Gabriel dimension of Cohen--Macaulay modules over hypersurfaces of countable Cohen--Macaulay representation type

We calculate the Krull–Gabriel dimension of the functor category of the (stable) category of maximal Cohen–Macaulay modules over hypersurfaces of countable Cohen– Macaulay representation type. We show that the Krull–Gabriel dimension is 0 if the hypersurface is of finite Cohen–Macaulay representation type and that is 2 if the hypersurface is of countable but not finite Cohen–Macaulay representation type.

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