Some results on test elements

DOI10.1017/S0013091500020502zbMath0973.13002MaRDI QIDQ4487694

Brian MacCrimmon, Ian M. Aberbach

Publication date: 22 June 2000

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

tight closuretest elements\(\mathbb{Q}\)-GorensteinF-regular domaingamma construction

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Integral closure of commutative rings and ideals (13B22) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (19)

F-singularities of pairs and inversion of adjunction of arbitrary codimension ⋮ SOME CONDITIONS FOR THE EQUIVALENCE OF WEAK AND STRONG F-REGULARITY ⋮ A generalization of tight closure and multiplier ideals ⋮ An interpretation of multiplier ideals via tight closure ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ Compatible ideals in ℚ-Gorenstein rings ⋮ TEST IDEALS IN RINGS WITH FINITELY GENERATED ANTI-CANONICAL ALGEBRAS ⋮ Geometric interpretation of tight closure and test ideals ⋮ Finitistic test ideals on numerically \(\mathbb{Q}\)-Gorenstein varieties ⋮ On the commutation of the test ideal with localization and completion ⋮ On a generalization of test ideals ⋮ \(F\)-signature exists ⋮ A characteristic \(p\) analogue of plt singularities and adjoint ideals ⋮ Relative test elements for tight closure ⋮ Discreteness and rationality of \(F\)-jumping numbers on singular varieties ⋮ Behavior of test ideals under smooth and étale homomorphisms. ⋮ Test ideals in non-$\mathbb{Q}$-Gorenstein rings ⋮ On the behavior of test ideals under finite morphisms ⋮ Applications of pseudocanonical covers to tight closure problems

Cites Work

• Tight closure of parameter ideals
• Rational singularities, with applications to algebraic surfaces and unique factorization
• F-rational rings have rational singularities
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• F-Regularity, Test Elements, and Smooth Base Change
• Test Ideals in Local Rings

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