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arXiv · 2406.02433

The Brian\c{c}on-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras

Sandra Rodríguez-Villalobos·Karl Schwede
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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 Brian\c{c}on-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.

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Sandra Rodríguez-Villalobos, Karl Schwede. 2024-06-04. The Brian\c{c}on-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras. https://arxiv.org/abs/2406.02433

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