Test ideals and base change problems in tight closure theory

DOI10.1090/S0002-9947-02-03162-8zbMath1019.13002arXivmath/0210278MaRDI QIDQ4779886

Florian Enescu, Ian M. Aberbach

Publication date: 28 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210278

zbMATH Keywords

characteristic \(p\)tight closurelocalizationF-rationalityHilbert-Kunz functionflat extensionsCS test ideal

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Étale and flat extensions; Henselization; Artin approximation (13B40)

Related Items (13)

A sufficient condition for strong $F$-regularity ⋮ Local cohomology and F-stability ⋮ Graded annihilators and tight closure test ideals ⋮ On the existence of 𝐹-thresholds and related limits ⋮ A less restrictive Briançon-Skoda theorem with coefficients ⋮ On the equality of test ideals ⋮ Finitistic test ideals on numerically \(\mathbb{Q}\)-Gorenstein varieties ⋮ A finiteness condition on local cohomology in positive characteristic ⋮ Phantom depth and flat base change ⋮ Behavior of test ideals under smooth and étale homomorphisms. ⋮ Strong test ideals ⋮ Strong test ideals associated to Cartier algebras ⋮ F-Pure Homomorphisms, StrongF-regularity, andF-injectivity

Cites Work

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• Tight closure and elements of small order in integral extensions
• Tight closure and strong test ideals
• On the behavior of F-rational rings under flat base change
• Openness of the F-rational locus and smooth base change
• On the commutation of the test ideal with localization and completion
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Localization of tight closure and modules of finite phantom projective dimension.
• On Noetherian Rings of Characteristic p
• Tight closure in F-rational rings
• F-Regularity, Test Elements, and Smooth Base Change
• SOME CONDITIONS FOR THE EQUIVALENCE OF WEAK AND STRONG F-REGULARITY
• Test Ideals in Local Rings
• Extension of weakly and strongly F-regular rings by flat maps
• Localization and test exponents for tight closure
• Behavior of test ideals under smooth and étale homomorphisms.
• Some results on tight closure and completion
• Strong test ideals

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