Ideals in a perfect closure, linear growth of primary decompositions, and tight closure
نویسندگان
چکیده
منابع مشابه
A Generalization of Tight Closure and Multiplier Ideals
We introduce a new variant of tight closure associated to any fixed ideal a, which we call a-tight closure, and study various properties thereof. In our theory, the annihilator ideal τ(a) of all a-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the correspondence of the ideal τ(a) and the multi...
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متن کاملGeometric Interpretation of Tight Closure and Test Ideals
We study tight closure and test ideals in rings of characteristic p 0 using resolution of singularities. The notions of F -rational and F regular rings are defined via tight closure, and they are known to correspond with rational and log terminal singularities, respectively. In this paper, we reformulate this correspondence by means of the notion of the test ideal, and generalize it to wider cl...
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Hara [Ha3] and Smith [Sm2] independently proved that in a normal Q-Gorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R,∆) of a normal ring R and an effective Q-Weil divisor ∆ on SpecR. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03420-8