An excellent $F$-pure ring of prime characteristic has a big tight closure test element

DOI10.1090/S0002-9947-10-05166-4zbMath1207.13003arXiv0907.2857MaRDI QIDQ3053480

Rodney Y. Sharp

Publication date: 29 October 2010

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

Full work available at URL: https://arxiv.org/abs/0907.2857

zbMATH Keywords

tight closuretest elementprime characteristicFrobenius homomorphismFrobenius skew polynomial ringF-pure ring

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Commutative Noetherian rings and modules (13E05) Local cohomology and commutative rings (13D45) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Complete rings, completion (13J10)

Related Items (7)

On the Frobenius complexity of determinantal rings ⋮ Big tight closure test elements for some non-reduced excellent rings ⋮ A sufficient condition for \(F\)-purity ⋮ Tight closure with respect to a multiplicatively closed subset of an \(F\)-pure local ring ⋮ Right and left modules over the Frobenius skew polynomial ring in theF-finite case ⋮ On the Graded Annihilators of Right Modules Over the Frobenius Skew Polynomial Ring ⋮ Graded annihilators and uniformly \(F\)-compatible ideals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local cohomological dimension in characteristic p
• The intersection homology \(D\)-module in finite characteristic
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• Uniform behaviour of the Frobenius closures of ideals generated by regular sequences
• Graded annihilators and tight closure test ideals
• On the commutation of the test ideal with localization and completion
• F-rational rings have rational singularities
• Bass Numbers of Local Cohomology Modules
• Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Parameter-test-ideals of Cohen–Macaulay rings
• F-Purity and Rational Singularity
• F-Regularity, Test Elements, and Smooth Base Change
• F-modules: applications to local cohomology and D-modules in characteristic p>0.
• Ideals in a perfect closure, linear growth of primary decompositions, and tight closure

This page was built for publication: An excellent $F$-pure ring of prime characteristic has a big tight closure test element