This book is a lightly edited version of the unpublished manuscript Maximal Cohen–
Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz …

Although there has been a lot of work and success lately in the theory of such modules, of
which this conference witnessed, it has remained mysterious-at least to the present author …

Motivated by recent work of Knorrer [17], Buchweitz, Greuel and Schreyer [9] who proved
that a hypersurface singularity R over C is of finite Cohen-Macaulay representation type if …

Let R be a commutative noetherian Cohen-Macaulay ring which admits a dualizing module.
We show that for any finitely generated R-module N there exists a maximal Cohen-Macaulay …

The study of Cohen-Macaulay modules over Noetherian local rings originates from the
theory of integral representations of finite groups (which, on its side, grew up from a very …

We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …

The trace of the canonical module (the canonical trace) determines the non-Gorenstein
locus of a local Cohen-Macaulay ring. We call a local Cohen-Macaulay ring nearly …

This paper contains two theorems concerning the theory of maximal Cohen–Macaulay
modules. The first theorem proves that certain Ext groups between maximal Cohen …

Given an artin algebra $\Lambda $ with an idempotent element $ a $ we compare the
algebras $\Lambda $ and $ a\Lambda a $ with respect to Gorensteinness, singularity …

We investigate relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …