2019 Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts
Geoffrey D. Dietz, Rebecca R.G.
J. Commut. Algebra 11(4): 511-533 (2019). DOI: 10.1216/JCA-2019-11-4-511


Let $R$ be a commutative, local, Noetherian ring. In a past article, the first author developed a theory of $R$-algebras, termed seeds, that can be mapped to balanced big Cohen-Macaulay $R$-algebras. In prime characteristic $p$, seeds can be characterized based on the existence of certain colon-killers, integral extensions of seeds are seeds, tensor products of seeds are seeds, and the seed property is stable under base change between complete, local domains. As a result, there exist directed systems of big Cohen-Macaulay algebras over complete, local domains. In this work, we will show that these properties can be extended to analogous results in equal characteristic zero. The primary tool for the extension will be the notion of ultraproducts for commutative rings as developed by Schoutens and Aschenbrenner.


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Geoffrey D. Dietz. Rebecca R.G.. "Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts." J. Commut. Algebra 11 (4) 511 - 533, 2019. https://doi.org/10.1216/JCA-2019-11-4-511


Published: 2019
First available in Project Euclid: 7 December 2019

zbMATH: 07147394
MathSciNet: MR4039980
Digital Object Identifier: 10.1216/JCA-2019-11-4-511

Primary: 13C14
Secondary: 13A35

Keywords: Big Cohen-Macaulay algebras , equal characteristic zero , tight closure , ultraproducts

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium


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Vol.11 • No. 4 • 2019
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