●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 ltiplicity
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

本書講述了緊閉包理論及其應用，緊閉包是一種通過約化到正特征來研究等特征環的方法。本書涵蓋了緊閉包的基本性質，包括各種類型的奇點，例如F正則奇點和F有理奇點；介紹了該理論的基本定理，包括Briancon-Skoda定理的各個版本、各種同調猜想以及關於約化群不變量的Hochster-Roberts/Boutot定理。此外，本書還給出了該理論的一些應用，包括大Cohen-Macaulay代數的存在性和各種一致Artin-Rees定理。本書適合於對交換環和交換代數感興趣的研究生閱讀，也可供相關研究人員參考。