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The Briançon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras

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  • Additional Information
    • Publication Date:
      2024
    • Collection:
      ArXiv.org (Cornell University Library)
    • Abstract:
      We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay algebras $R \mapsto B$, that the associated big Cohen-Macaulay closure operation on ideals $I \mapsto I B \cap R$ necessarily satisfies the Briançon-Skoda type property. The proof combines arguments of Lipman-Teissier, Hochster, Ma, and Hochster-Huneke. Specializing to mixed characteristic, and utilizing a result of Bhatt on absolute integral closures, this recovers a slight strengthening of a result of Heitmann. ; Minor changes and typos fixed, 13 pages, to appear in the Michigan Mathematical Journal
    • Relation:
      http://arxiv.org/abs/2406.02433
    • Online Access:
      http://arxiv.org/abs/2406.02433
    • Accession Number:
      edsbas.F65C0BE2