For a finitely generated A-module M we define the dimension filtration M = {Mi}0≤i≤d, d = dimA M, where Mi denotes the largest submodule of M of dimension ≤ i. Several properties of this filtration are investigated. In particular, in case the local ring (A,m) possesses a dualizing complex, then this filtration occurs as the filtration of a spectral sequence related to duality. Furthermore, we c...

This research began as an effort to determine exactly which one-dimensional local rings have indecomposable finitely generated modules of arbitrarily large constant rank. The approach, which uses a new construction of indecomposable modules via the bimodule structure on certain Ext groups, turned out to be effective mainly for hypersurface singularities. The argument was eventually replaced by ...

We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen–Macaulay modules, which we review in an Appendix.