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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On arithmetic Macaulayfication of Noetherian rings


Author: Takesi Kawasaki
Journal: Trans. Amer. Math. Soc. 354 (2002), 123-149
MSC (1991): Primary 13A30; Secondary 13D45, 13H10
Published electronically: June 6, 2001
MathSciNet review: 1859029
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Abstract:

The Rees algebra is the homogeneous coordinate ring of a blowing-up. The present paper gives a necessary and sufficient condition for a Noetherian local ring to have a Cohen-Macaulay Rees algebra: A Noetherian local ring has a Cohen-Macaulay Rees algebra if and only if it is unmixed and all the formal fibers of it are Cohen-Macaulay. As a consequence of it, we characterize a homomorphic image of a Cohen-Macaulay local ring. For non-local rings, this paper gives only a sufficient condition. By using it, however, we obtain the affirmative answer to Sharp's conjecture. That is, a Noetherian ring having a dualizing complex is a homomorphic image of a finite-dimensional Gorenstein ring.


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Additional Information

Takesi Kawasaki
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Hachioji-shi Minami-Ohsawa 1-1, Tokyo 192-0397, Japan
Email: kawasaki@comp.metro-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02817-3
PII: S 0002-9947(01)02817-3
Keywords: Arithmetic Macaulayfication, Cohen-Macaulay rings, dualizing complex, excellent rings, formal fibers, local cohomology, Macaulayfication, Rees algebra
Received by editor(s): February 15, 2000
Published electronically: June 6, 2001
Additional Notes: The author is partially supported by Grant-in-Aid for Co-Operative Research
Article copyright: © Copyright 2001 American Mathematical Society