F-rational rings have rational singularities
F-rational rings have rational singularities
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F-有理环具有有理奇点
DOI：
10.1353/ajm.1997.0007
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发表时间：
1997
影响因子：
1.7
通讯作者：
Karen E. Smith
中科院分区：
文献类型：
--
作者：
Karen E. Smith
证明了一个由任意参数系生成的理想是紧闭的素特征的优良局部环必是伪随机的。证明中的一个关键点是F-有理局部环的一个特征：Cohen-Macaulay局部环（R，m）中的局部上同调模Hdm（R）（其中d是R的维数）在Frobenius映射的自然作用下没有稳定的子模.对特征为零的域上的代数生成代数进行了模拟，得到了[inline-graphic xmlns：xlink=”http://www.w3.org/1999/xlink“xlink：href=“01 i”/]上代数簇的有理奇点的合理可检验的紧闭包检验，而不涉及去奇异化.
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.