Cohen-Macaulay modules over Cohen-Macaulay rings. (English) Zbl 0745.13003

London Mathematical Society Lecture Note Series. 146. Cambridge (UK): Cambridge University Press. 177 p. (1990).
In these lecture notes the author gives an approach for the classification of maximal Cohen-Macaulay modules over a local Henselian ring of an isolated singularity using the Auslander-Reiten theory (Auslander-Reiten sequences, quivers up to the Brauer-Thrall theorem). Several cases are treated as: simple singularities, the one-dimensional and the two-dimensional case, modules on quadrics, on toric singularities.
Reviewer: G.Pfister (Berlin)


13C14 Cohen-Macaulay modules
13-02 Research exposition (monographs, survey articles) pertaining to commutative algebra
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G50 Cohen-Macaulay modules in associative algebras