On the Hartshorne–Speiser–Lyubeznik theorem about Artinian modules with a Frobenius action

DOI10.1090/S0002-9939-06-08606-0zbMath1116.13003arXivmath/0605330OpenAlexW1782166256MaRDI QIDQ3420038

Rodney Y. Sharp

Publication date: 1 February 2007

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

Full work available at URL: https://arxiv.org/abs/math/0605330

zbMATH Keywords

prime characteristicFrobenius homomorphismArtinian module

Mathematics Subject Classification ID

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) Associative rings and algebras arising under various constructions (16S99)

Related Items (14)

Frobenius test exponent for ideals generated by filter regular sequences ⋮ On the uniform bound of Frobenius test exponents ⋮ Local Cohomology—An Invitation ⋮ Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings ⋮ Some extensions of Hilbert-Kunz multiplicity ⋮ Tight closure of parameter ideals in local rings \(F\)-rational on the punctured spectrum ⋮ On the Frobenius closure of parameter ideals in local rings F-injective on the punctured spectrum ⋮ Big tight closure test elements for some non-reduced excellent rings ⋮ Notes on the Frobenius test exponents ⋮ Right and left modules over the Frobenius skew polynomial ring in theF-finite case ⋮ Upper bound of multiplicity in prime characteristic ⋮ A sufficient condition for the finiteness of Frobenius test exponents ⋮ Estimates forF-jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers ⋮ Homological properties of pinched Veronese rings

Cites Work

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• Codimension and multiplicity
• Tight closure test exponents for certain parameter ideals
• Local cohomological dimension in characteristic p
• Tight closure of parameter ideals
• Uniform behaviour of the Frobenius closures of ideals generated by regular sequences
• Bass Numbers of Local Cohomology Modules
• F-modules: applications to local cohomology and D-modules in characteristic p>0.
• Test Ideals in Local Rings
• Characterizations of Regular Local Rings of Characteristic p
• Localization and test exponents for tight closure

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