Transactions of the American Mathematical Society

Author(s): Takesi Kawasaki
Journal: Trans. Amer. Math. Soc. 360 (2008), 2709-2739.
MSC (2000): Primary 13D03; Secondary 13A30, 13F40, 13H10
Posted: September 25, 2007
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Abstract: The notion of the Cousin complex of a module was given by Sharp in 1969. It wasn't known whether its cohomologies are finitely generated until recently. In 2001, Dibaei and Tousi showed that the Cousin cohomologies of a finitely generated

-module

are finitely generated if the base ring

is local, has a dualizing complex,

satisfies Serre's

-condition and is equidimensional. In the present article, the author improves their result. He shows that the Cousin cohomologies of

are finitely generated if

is universally catenary, all the formal fibers of all the localizations of

are Cohen-Macaulay, the Cohen-Macaulay locus of each finitely generated

-algebra is open and all the localizations of

are equidimensional. As a consequence of this, he gives a necessary and sufficient condition for a Noetherian ring to have an arithmetic Macaulayfication.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13D03, 13A30, 13F40, 13H10

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

DOI: 10.1090/S0002-9947-07-04418-2
PII: S 0002-9947(07)04418-2
Keywords: Arithmetic Macaulayfication, Cohen-Macaulay ring, Cousin complex, excellent ring
Received by editor(s): October 8, 2003
Received by editor(s) in revised form: September 4, 2006
Posted: September 25, 2007
Additional Notes: This work was supported by the Japan Society for the Promotion of Science (the Grant-in-Aid for Scientific Research (C)(2)~13640034)
Copyright of article: Copyright 2007, American Mathematical Society

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