Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension

DOI10.1307/mmj/1220879393zbMath1222.13005arXiv0708.0537OpenAlexW2016036716MaRDI QIDQ841514

Ian M. Aberbach, Florian Enescu

Publication date: 17 September 2009

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.0537

zbMATH Keywords

characteristic \(p\)formally unmixed local ringsHilbert-Kunz multiplicities

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (16)

Bounds on the Hilbert-Kunz multiplicity ⋮ 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 ⋮ The Hilbert-Kunz density functions of quadric hypersurfaces ⋮ CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE ⋮ \(F\)-signature and Hilbert-Kunz multiplicity: a combined approach and comparison ⋮ Upper semi-continuity of the Hilbert–Kunz multiplicity ⋮ The zonotope of a root system ⋮ Hilbert-Kunz multiplicity of fibers and Bertini theorems ⋮ Equimultiplicity theory of strongly \(F\)-regular rings ⋮ 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

Cites Work

• Unnamed Item
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• Cohen-Macaulay local rings of maximal embedding dimension
• Tight closure of parameter ideals
• Hilbert-Kunz functions of cubic curves and surfaces
• Notes on the Hilbert-Kunz function.
• The \(F\)-signature and strong \(F\)-regularity.
• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• On the upper semi-continuity of the Hilbert-Kunz multiplicity
• Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
• Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular
• Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
• Hilbert-Kunz Multiplicity of Three-Dimensional Local Rings
• BOUNDS ON MULTIPLICITIES OF LOCAL RINGS
• On rings with small Hilbert-Kunz multiplicity
• Extension of weakly and strongly F-regular rings by flat maps
• Some results on tight closure and completion

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