Behavior of test ideals under smooth and etale homomorphisms

JOURNAL OF ALGEBRA

卷:247

Article

Bravo, A ; Smith, KE

关键词: tight closure;    test ideals;    Frobenius action;   

DOI  :  10.1006/jabr.2001.9010

来源: Elsevier

【 摘 要 】

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 tau(A)D = tau(D), assuming that all residue fields of A at maximal ideals are per-feet 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 tau(A)D = tau(D). More generally, this last result holds under the assumption that the closed fiber of h: (A, in) 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. (C) 2002 Elsevier Science.

【 授权许可】

Free