Memoirs of the American Mathematical Society 1993; 91 pp; softcover Volume: 103 ISBN10: 0821825569 ISBN13: 9780821825563 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/103/490
 This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly CohenMacaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to wellbehaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic \(p\). The book would be suitable for use in an advanced graduate course in commutative algebra. Readership Algebraists and algebraic geometers interested in a deeper understanding of commutative algebra. Table of Contents  Minheight and the weak CohenMacaulay property
 Acyclicity criteria with denominators for complexes of modules
 Vanishing theorems for maps of homology via phantom acyclicity
 Regular closure
 Intersection theorems via phantom acyclicity
