本书讲述了紧闭包理论及其应用，紧闭包是一种通过约化到正特征来研究等特征环的方法。本书涵盖了紧闭包的基本性质，包括各种类型的奇点，例如F正则奇点和F有理奇点；介绍了该理论的基本定理，包括Brian?on—Skoda定理的各个版本、各种同调猜想以及关于约化群不变量的Hochster—Roberts/Boutot定理。此外，本书还给出了该理论的一些应用，包括大Cohen—Macaulay代数的存在性和各种一致Artin—Rees定理。本书适合于对交换环和交换代数感兴趣的研究生阅读，也可供相关研究人员参考。
Acknowledgements
Introduction
Relationship Chart
Chapter 0.A Prehistory of Tight Closure
Chapter 1.Basic Notions
Chapter 2.Test Elements and the Persistence of Tight Closure
Chapter 3.Colon-Capturing and Direct Summands of Regular Rings
Chapter 4.F-Rational Rings and Rational Singularities
Chapter 5.Integral Closure and Tight Closure
Chapter 6.The Hilbert-Kunz Multiplicity
Chapter 7.Big Cohen-Macaulay Algebras
Chapter 8.Big Cohen-Macaulay Algebras Ⅱ
Chapter 9.Applications of Big Cohen-Macaulay Algebras
Chapter 10.Phantom Homology
Chapter 11.Uniform Artin-Rees Theorems
Chapter 12.The Localization Problem
Chapter 13.Regular Base Change
Appendix 1: The Notion of Tight Closure in Equal Characteristic Zero (by M.Hochster)
Appendix 2: Solutions to the Exercises
Bibliography
