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A characterization of closure operations that induce big Cohen-Macaulay modules
Author:
Geoffrey D. Dietz
Journal:
Proc. Amer. Math. Soc. 138 (2010), 3849-3862
MSC (2000):
Primary 13C14; Secondary 13A35
Posted:
May 24, 2010
MathSciNet review:
2679608
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Additional Information
Abstract: The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module  over a complete local domain  . Conversely, we show that if such a  exists over  , then there exists a closure operation that satisfies the given axioms.
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(2008h:13021), http://dx.doi.org/10.1090/S0002-9947-07-04252-3
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pp. 103–172. MR 1266182
(95a:13011), http://dx.doi.org/10.1090/conm/159/01508
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M. HOCHSTER, Foundations of tight closure theory, lecture notes available at http://www.math.lsa.umich.edu/
 hochster/mse.html.
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Melvin
Hochster and Craig
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algebras, Ann. of Math. (2) 135 (1992), no. 1,
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(1994), no. 4, 599–670. MR 1297848
(95k:13002)
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M. HOCHSTER and C. HUNEKE, Tight Closure in Equal Characteristic Zero, preprint available at http://www.math.lsa.umich.edu/ hochster/msr.html.
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E. Smith, Tight closure of parameter ideals, Invent. Math.
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(94k:13006), http://dx.doi.org/10.1007/BF01231753
- [D]
- G. DIETZ, Big Cohen-Macaulay algebras and seeds, Trans. Amer. Math. Soc. 359 (2007), no. 12, 5959-5989. MR 2336312 (2008h:13021)
- [Ho1]
- M. HOCHSTER, Topics in the homological theory of modules over commutative rings, CBMS Regional Conf. Ser. in Math. 24, Amer. Math. Soc., Providence, RI, 1975. MR 0371879 (51:8096)
- [Ho2]
- M. HOCHSTER, Solid closure, in: Commutative Algebra: Syzygies, Multiplicities and Birational Algebra, Contemp. Math. 159, Amer. Math. Soc., Providence, RI, 1994, 103-172. MR 1266182 (95a:13011)
- [Ho3]
- M. HOCHSTER, Foundations of tight closure theory, lecture notes available at http://www.math.lsa.umich.edu/hochster/mse.html.
- [HH1]
- M. HOCHSTER and C. HUNEKE, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31-116. MR 1017784 (91g:13010)
- [HH2]
- M. HOCHSTER and C. HUNEKE, Infinite integral extensions and big Cohen-Macaulay algebras, Annals of Math. 135 (1992), 53-89. MR 1147957 (92m:13023)
- [HH3]
- M. HOCHSTER and C. HUNEKE, Tight closure of parameter ideals and splitting in module-finite extensions, J. Algebraic Geom. 3 (1994), no. 4, 599-670. MR 1297848 (95k:13002)
- [HH4]
- M. HOCHSTER and C. HUNEKE, Tight Closure in Equal Characteristic Zero, preprint available at http://www.math.lsa.umich.edu/ hochster/msr.html.
- [Sm]
- K.E. SMITH, Tight closure of parameter ideals, Invent. Math. 115 (1994), 41-60. MR 1248078 (94k:13006)
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Additional Information
Geoffrey D. Dietz
Affiliation:
Department of Mathematics, Gannon University, Erie, Pennsylvania 16541
Email:
gdietz@member.ams.org
DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10417-3
PII:
S 0002-9939(2010)10417-3
Received by editor(s):
October 28, 2009
Received by editor(s) in revised form:
January 30, 2010
Posted:
May 24, 2010
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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