On the splitting of big Cohen-Macaulay modules Original Research Article

In this article it is noted that, in equicharacteristic zero, the existence of small Cohen-Macaulay modules may be reduced to whether countably generatd infinite syzygies over cyclic hypersurface rings have finite type direct summands (Theorem 1.9). In the special case of simple singularities it is then shown (Corollary 5.2) that countably generated infinite syzygies decompose into direct sums of finitely generated modules.