A Characterization of F -Regularity in Terms of F -Purity
A Characterization of F -Regularity in Terms of F -Purity
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用 F 纯度表征 F 正则性
DOI：
10.1007/978-1-4612-3660-3_11
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发表时间：
1989
影响因子：
0.9
通讯作者：
Kei
中科院分区：
文献类型：
--
作者：
R. Fedder;Kei
近年来，一些非常有趣的定理已经被证明独立使用复分析技术，或者，使用减少到特征p技术（依赖于特殊性质的弗罗贝纽斯同态）。特别地，Hochster和Roberts [12]证明了作用在正则环R上的群G的不变量的环R G必然是Cohen-Macaulay，通过一个论证，该论证利用了R G是R在特征0中的直和项的事实，并且因此，在还原为特征p之后，Frobenius同态对于“几乎所有p”都是特别好的。不久之后，利用Grauert-Riemenschneider消失定理，Boutot [1]证明了一个更强的结果-在仿射和解析情形下，具有有理奇点的环的直和项（特征为0）必然具有有理奇点。
In recent years, some very interesting theorems have been proven independently using complex analytic techniques or, alternatively, using reduction to characteristic p techniques (relying on special properties of the Frobenius homomorphism). In particular, Hochster and Roberts [12] proved that the ring R G of invariants of a group G acting on a regular ring R is necessarily Cohen-Macaulay by an argument which exploits the fact that R G is a direct summand of R in characteristic 0 and that, therefore, after reduction to characteristic p, the Frobenius homomorphism is especially well-behaved for “almost all p”. Not long after, using the Grauert-Riemenschneider vanishing theorem, Boutot [1] proved an even stronger result— in the affine and analytic cases, a direct summand (in characteristic 0) of a ring with rational singularity necessarily has a rational singularity.