Notes on the Hilbert-Kunz function.

DOI10.1016/S0021-8693(03)00233-3zbMath1091.13504MaRDI QIDQ1400184

Douglas A. Hanes

Publication date: 13 August 2003

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

Hilbert-Kunz multiplicityHilbert-Kunz functionsHilbert-Samuel functionsmixed Hilbert function

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 (14)

Uniform Lech’s inequality ⋮ Hilbert-Kunz density function and asymptotic Hilbert-Kunz multiplicity for projective toric varieties ⋮ Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension ⋮ A New Version of α-Tight Closure ⋮ On rings with small Hilbert-Kunz multiplicity ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ Asymptotic Hilbert-Kunz multiplicity ⋮ On the Hilbert-Samuel coefficients of Frobenius powers of an ideal ⋮ Hilbert-Kunz multiplicity of products of ideals ⋮ Observations on the \(F\)-signature of local rings of characteristic \(p\) ⋮ Hilbert–Kunz multiplicity of the powers of an ideal ⋮ Asymptotic Lech's inequality ⋮ Lower bounds on Hilbert–Kunz multiplicities and maximal F-signatures ⋮ The rationality of the Hilbert-Kunz multiplicity in graded dimension two

Cites Work

• Gorenstein rings and modules with high numbers of generators
• Thin algebras of embedding dimension three
• Some surprising Hilbert-Kunz functions
• Hilbert-Kunz multiplicity and an inequality between multiplicity and colength
• The Hilbert-Kunz function
• Note on multiplicities of ideals
• Some criteria for the Gorenstein property
• Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
• THE LINEAR SYZYGIES OF GENERIC FORMS
• On Noetherian Rings of Characteristic p
• A Problem on Noetherian Local Rings of Characteristic p
• BOUNDS ON MULTIPLICITIES OF LOCAL RINGS
• Characterizations of Regular Local Rings of Characteristic p

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