The spectrum of a category of maximal Cohen-Macaulay modules

We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay modules over a complete Cohen-Macaulay local ring. We define a topology on the space of isomorphism classes of indecomposable maximal Cohen-Macaulay modules and investigate the topological structure. We also calculate the Cantor-Bendixson rank for a ring which is of CM_±finite representation type.