On the Hilbert-Samuel coefficients of Frobenius powers of an ideal

DOI10.1090/proc/16666arXiv2203.10173OpenAlexW4387738071MaRDI QIDQ6203186

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Publication date: 27 February 2024

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

Full work available at URL: https://arxiv.org/abs/2203.10173

zbMATH Keywords

Hilbert-Kunz functionHilbert-Kunz multiplicityFrobenius powergeneralized Hilbert-Kunz multiplicitygeneralized Hilbert-Kunz functionHilbert-Samuel coefficientsface ring of simplicial complex

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Cohen-Macaulay modules (13C14) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Cites Work

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• Hilbert-Kunz function of monomial ideals and binomial hypersurfaces
• The Hilbert-Kunz function
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• Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings
• Form rings and regular sequences
• Hilbert Coefficients and the Depths of Associated Graded Rings
• Absolutely superficial sequences
• A 𝑑-dimensional extension of a lemma of Huneke’s and formulas for the Hilbert coefficients
• A bound on the reduction number of a primary ideal
• Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex
• Hilbert–Kunz multiplicity of the powers of an ideal
• Characterizations of Regular Local Rings of Characteristic p

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