On rings with small Hilbert-Kunz multiplicity

DOI10.1090/S0002-9939-04-07469-6zbMath1099.13009arXivmath/0308022MaRDI QIDQ4813665

Manuel Blickle, Florian Enescu

Publication date: 13 August 2004

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

Full work available at URL: https://arxiv.org/abs/math/0308022

zbMATH Keywords

regular ringHilbert-Kunz multiplicity\(F\)-rational ring

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (20)

Bounds on the Hilbert-Kunz multiplicity ⋮ Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension ⋮ Equimultiplicity in Hilbert-Kunz theory ⋮ On the existence of 𝐹-thresholds and related limits ⋮ Hilbert-Kunz multiplicities and \(F\)-thresholds ⋮ On lower bounds for \(s\)-multiplicities ⋮ Globalizing F-invariants ⋮ CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE ⋮ \(F\)-signature and Hilbert-Kunz multiplicity: a combined approach and comparison ⋮ \(F\)-signature exists ⋮ On the upper semi-continuity of the Hilbert-Kunz multiplicity ⋮ Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings ⋮ Observations on the \(F\)-signature of local rings of characteristic \(p\) ⋮ Characterizations of regular local rings in positive characteristics ⋮ Upper semi-continuity of the Hilbert–Kunz multiplicity ⋮ Hilbert-Kunz multiplicity of fibers and Bertini theorems ⋮ The shape of Hilbert-Kunz functions ⋮ New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension ⋮ Lower bounds on Hilbert–Kunz multiplicities and maximal F-signatures ⋮ The rationality of the Hilbert-Kunz multiplicity in graded dimension two

Cites Work

• Unnamed Item
• Hilbert-Kunz functions of cubic curves and surfaces
• Notes on the Hilbert-Kunz function.
• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
• Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular
• Multiplicity and tight closures of parameters

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