^-REGULARITY, TEST ELEMENTS, AND SMOOTH BASE CHANGE
^-REGULARITY, TEST ELEMENTS, AND SMOOTH BASE CHANGE
复制标题
^-规律性、测试元素和平滑的基础变化
DOI：
10.1078/1439-6092-00057
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发表时间：
2010
影响因子：
1.6
通讯作者：
C. Huneke
中科院分区：
文献类型：
--
作者：
M. Hochster;C. Huneke
本文讨论了正特征线上的紧闭包理论。经过前五节的大量前期工作，包括Gorenstein环的F-合理性和F-正则性的处理，在§6中发展了一个非常广泛适用的紧闭包的检验元理论，然后在§7中应用该理论证明了紧闭包和F正则性在许多情况下都与光滑基变交换（其中“光滑的”用于表示具有几何规则纤维的平坦的）。例如，在§6中表明，对于特征为p的优良局部环上的本质上有限型的约化环R，如果c不在R的任何极小素数中，并且Rc是正则的，则c有一个幂是测试元。§7证明了如果S是具有正则纤维的平坦f {-代数，R是F-正则的，则S是F-正则的。表明紧密封闭与平稳的碱基变化互换的一般问题仍然是开放的，但在这里被简化为表明紧密封闭与局部化互换。
This paper deals with tight closure theory in positive characteristic. After a good deal of preliminary work in the first five sections, including a treatment of F-rationality and a treatment of F-regularity for Gorenstein rings, a very widely applicable theory of test elements for tight closure is developed in §6 and is then applied in §7 to prove that both tight closure and F-regularity commute with smooth base change under many circumstances (where "smooth" is used to mean flat with geometrically regular fibers). For example, it is shown in §6 that for a reduced ring R essentially of finite type over an excellent local ring of characteristic p , if c is not in any minimal prime of R and Rc is regular, then c has a power that is a test element. It is shown in §7 that if S is a flat /{-algebra with regular fibers and R is F-regular then S is F-regular. The general problem of showing that tight closure commutes with smooth base change remains open, but is reduced here to showing that tight closure commutes with localization.