Topics in the Homological Theory of Modules over Commutative Rings

Introduction Preliminaries Some open questions Consequences of the existence of Cohen-Macaulay modules Modifications and the existence of big Cohen-Macaulay modules in characteristic $p>0$ Henselian rings, M. Artin’s approximation theorem, and big Cohen-Macaulay modules over fields of characteristic 0 Depth-sensitivity theorems and exactness criteria Modules of projective dimension 2, generic modules of finite projective dimension, and the Buchsbaum-Eisenbud structure theorems Linear algebraic groups Applications of homological methods and some more open questions Supplement References.