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Big Cohen-Macaulay algebras and seeds


Author: Geoffrey D. Dietz
Journal: Trans. Amer. Math. Soc. 359 (2007), 5959-5989
MSC (2000): Primary 13C14, 13A35; Secondary 13H10, 13B99
DOI: https://doi.org/10.1090/S0002-9947-07-04252-3
Published electronically: June 26, 2007
MathSciNet review: 2336312
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Abstract: In this article, we delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big Cohen-Macaulay algebra. We will also strengthen Hochster and Huneke's ``weakly functorial" existence result for big Cohen-Macaulay algebras by showing that the seed property is stable under base change between complete local domains of positive characteristic. We also show that every seed over a positive characteristic ring $ (R,m)$ maps to a balanced big Cohen-Macaulay $ R$-algebra that is an absolutely integrally closed, $ m$-adically separated, quasilocal domain.


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Additional Information

Geoffrey D. Dietz
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-0315
Address at time of publication: Department of Mathematics, Gannon University, Erie, Pennsylvania 16541
Email: gdietz@member.ams.org

DOI: https://doi.org/10.1090/S0002-9947-07-04252-3
Keywords: Big Cohen-Macaulay algebras, tight closure
Received by editor(s): August 22, 2005
Published electronically: June 26, 2007
Additional Notes: The author was supported in part by a VIGRE grant from the National Science Foundation.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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