Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: June 26, 2007
MathSciNet review: 2336312
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13C14, 13A35, 13H10, 13B99

Retrieve articles in all journals with MSC (2000): 13C14, 13A35, 13H10, 13B99


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: http://dx.doi.org/10.1090/S0002-9947-07-04252-3
PII: S 0002-9947(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.