F-rational rings have rational singularities 论文

摘要

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 H d m ( 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.