Behavior of Test Ideals under Smooth and Étale Homomorphisms
Behavior of Test Ideals under Smooth and Étale Homomorphisms
复制标题
Smooth 和 Étale 同态下测试理想的行为
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Karen E. Smith
中科院分区：
文献类型：
--
作者：
A. Bravo;Karen E. Smith
研究了素特征的优良约化环的测试理想在基变换下的行为。结果表明，如果h：A → D是光滑同态，则τAD = τD，假设A在极大理想处的所有剩余域都是完美的，并且测试理想的形成与局部化互换。还证明了：如果h：（A，m）→ D是Gorenstein正规环的有限平坦同态，余维为1，则τAD = τD.更一般地说，最后一个结果在假设h：（A，m）→ D的闭纤维是Gorenstein的情况下成立，只要我们知道A和S的剩余域的内射壳中零的紧闭包和零的有限紧闭包相等。
We investigate the behavior of the test ideal of an excellent reduced ring of prime characteristic under base change. It is shown that if h: A → D is a smooth homomorphism, then τAD = τD, assuming that all residue fields of A at maximal ideals are perfect and that formation of the test ideal commutes with localization. It is also shown that if h: (A, m) → D is a finite flat homomorphism of Gorenstein normal rings, etale in codimension 1, then τAD = τD. More generally, this last result holds under the assumption that the closed fiber of h: (A, m) → D is Gorenstein, provided one knows that the tight closure of zero and the finitistic tight closure of zero in the injective hulls of the residue fields of A and S are equal.