Tight closure and strong test ideals
نویسندگان
چکیده
منابع مشابه
Geometric 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...
متن کاملA 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...
متن کاملLocalization and Test Exponents for Tight Closure
We introduce the notion of a test exponent for tight closure, and explore its relationship with the problem of showing that tight closure commutes with localization, a longstanding open question. Roughly speaking, test exponents exist if and only if tight closure commutes with localization: mild conditions on the ring are needed to prove this. We give other, independent, conditions that are nec...
متن کاملStrong Test Modules and Multiplier Ideals
We introduce the notion of strong test module and show that a large number of such modules appear in the tight closure theory of complete domains: the test ideal (this has already been known), the parameter test module, and the module of relative test elements. They also appear as certain multiplier ideals, a concept of interest in algebraic geometry.
متن کاملAn Interpretation of Multiplier Ideals via Tight Closure
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: Journal of Pure and Applied Algebra
سال: 1997
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00053-4