Tight Closure’s Failure to Localize - a Self-Contained Exposition

Abstract

AbstractBrenner and Monsky have given a negative solution to the localization problem for tight closure. Here I give a treatment of our counterexample that uses only linear algebra, material from an introductory abstract algebra course, and a little local cohomology developed ab initio. But most of this machinery, useful as it is for understanding the counterexample, may be dispensed with; in this paper the author gives a treatment of the example, using only linear algebra, material from an introductory abstract algebra course, and a little local cohomology developed ab initio.KeywordsTight ClosureSelf-contained ExpositionAbstract Algebra CourseLocal CohomologyHilbert-Kunz MultiplicityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.