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Test ideals and base change problems in tight closure theory


Authors: Ian M. Aberbach and Florian Enescu
Journal: Trans. Amer. Math. Soc. 355 (2003), 619-636
MSC (2000): Primary 13A35; Secondary 13B40
DOI: https://doi.org/10.1090/S0002-9947-02-03162-8
Published electronically: October 9, 2002
MathSciNet review: 1932717
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Abstract: Test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand. Our paper presents results regarding this behavior under flat maps with reasonably nice (but far from smooth) fibers. This involves analyzing, in depth, a special type of ideal of test elements, called the CS test ideal. Besides providing new results, the paper also contains extensions of a theorem by G. Lyubeznik and K. E. Smith on the completely stable test ideal and of theorems by F. Enescu and, independently, M. Hashimoto on the behavior of $F$-rationality under flat base change.


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Additional Information

Ian M. Aberbach
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: aberbach@math.missouri.edu

Florian Enescu
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109; Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Address at time of publication: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: fenescu@umich.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03162-8
Received by editor(s): October 30, 2001
Published electronically: October 9, 2002
Additional Notes: The first author was partially supported by the NSF and by the University of Missouri Research Board. The second author thanks the University of Michigan for support through the Rackham Predoctoral Fellowship
Article copyright: © Copyright 2002 American Mathematical Society

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