The Briancon-Skoda Theorem via weak functoriality of big Cohen-Macaulay algebras
Abstract
We prove that, given a sufficiently functorial assignment from rings to big Cohen-Macaulay algebras R B, that the associated big Cohen-Macaulay closure operation on ideals I I B R necessarily satisfies the Briancon-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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