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arXiv · 2405.15075

Hilbert-Kunz Multiplicity of Fiber Product Rings and Nagata Idealizations

Victor H. Jorge-Pérez·Paulo D. C. Martins·J. A. Lima
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Abstract

The main purpose of this paper is to provide formulas for the Hilbert-Kunz multiplicity of fiber product rings and Nagata idealizations. We give explicit formulas for the Hilbert-Kunz multiplicity of a fiber product $R \times_T S$, where $R$, $S$, and $T$ are Noetherian local rings sharing the same characteristic and residue field. We compute the Hilbert-Kunz multiplicity of a general Nagata idealization $R \ltimes M$, where $M$ is a finitely generated $R$-module. Additionally, we provide examples, structural results and establish new bounds for the Hilbert-Kunz multiplicity.

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Victor H. Jorge-Pérez, Paulo D. C. Martins, J. A. Lima. 2024-05-23. Hilbert-Kunz Multiplicity of Fiber Product Rings and Nagata Idealizations. https://arxiv.org/abs/2405.15075

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