Tight Closure in Equal Characteristic Zero: With an Introduction to the Characteristic P Theory

The main objective of this monograph is to lay the foundations of tight closure theory for Noetherian rings containing a field of characteristic 0. It has been more than ten years since the authors first began work on tight closure. In that time they have published many articles on the topic. This remarkably potent method has led to a number of generalizations of old theorems, improved proofs, and a host of beautiful new results. This monograph will serve as a marvelous introduction to tight closure for both researchers and graduate students in commutative algebra.