Seminar

This talk is based on joint work with Hailong Dao. Let R be a Cohen-Macaulay local ring. Recall that R is said to have finite CM-representation type if there are only finitely many isomorphism classes of indecomposable (maximal) Cohen-Macaulay R-modules. In this case, clearly there exists a finitely generated R-module M out of which all Cohen-Macaulay R-modules are built by taking direct sums and direct summands. The converse is also true, namely, such a module M does not exist if R has infinite CM-representation type. Now a natural question arises: what if we also allow taking syzygies and a fixed number of extensions? This is a main problem which we deal with in this talk