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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Faltings' annihilator theorem


Author: Takesi Kawasaki
Journal: Proc. Amer. Math. Soc. 136 (2008), 1205-1211
MSC (1991): Primary 13D45; Secondary 13C15, 14B15
Published electronically: November 23, 2007
MathSciNet review: 2367094
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Abstract: In the present article, the author shows that Faltings' annihilator theorem holds for any Noetherian ring $ A$ if $ A$ is universally catenary; all the formal fibers of all the localizations of $ A$ are Cohen-Macaulay; and the Cohen-Macaulay locus of each finitely generated $ A$-algebra is open.


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Additional Information

Takesi Kawasaki
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0397, Japan
Email: kawasaki@tmu.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09128-9
PII: S 0002-9939(07)09128-9
Keywords: Annihilators of local cohomologies, Cousin complex, Artin-Rees theorem, Brian\c{c}on-Skoda theorem
Received by editor(s): September 15, 2006
Received by editor(s) in revised form: January 11, 2007
Published electronically: November 23, 2007
Additional Notes: This work was supported by the Japan Society for the Promotion of Science (the Grant-in-Aid for Scientific Researches (C)(2) 16540032)
Dedicated: Dedicated to Professor Shiro Goto on the occasion of his sixtieth birthday
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.