Abstract

It is proved that an excellent local ring of prime characteristic in which a single ideal generated by any system of parameters is tightly closed must be pseudorational. A key point in the proof is a characterization of F-rational local rings as those Cohen-Macaulay local rings (R, m) in which the local cohomology module Hdm (R) (where d is the dimension of R) have no submodules stable under the natural action of the Frobenius map. An analog for finitely generated algebras over a field of characteristic zero is developed, which yields a reasonably checkable tight closure test for rational singularities of an algebraic variety over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], without reference to a desingularization.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 159-180
Launched on MUSE
1997-02-01
Open Access
No
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