CBMS Regional Conference Series in Mathematics 1975; 75 pp; softcover Number: 24 Reprint/Revision History: fifth printing 2001 ISBN10: 0821816748 ISBN13: 9780821816745 List Price: US$21 Member Price: US$16.80 All Individuals: US$16.80 Order Code: CBMS/24
 This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role "big" CohenMacaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader. Readership Table of Contents  Introduction
 Preliminaries
 Some open questions
 Consequences of the existence of CohenMacaulay modules
 Modifications and the existence of big CohenMacaulay modules in characteristic \(p>0\)
 Henselian rings, M. Artin's approximation theorem, and big CohenMacaulay modules over fields of characteristic 0
 Depthsensitivity theorems and exactness criteria
 Modules of projective dimension 2, generic modules of finite projective dimension, and the BuchsbaumEisenbud structure theorems
 Linear algebraic groups
 Applications of homological methods and some more open questions
 Supplement
 References
