Illinois Journal of Mathematics

On finiteness properties of local cohomology modules over Cohen–Macaulay local rings

Ken-ichiroh Kawasaki

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Abstract

Let $A$ be a Cohen-Macaulay local ring which contains a field $k$, and let $I \subseteq A$ be an ideal generated by polynomials in a system of parameters of $A$ with coefficients in $k$. In this paper, we shall prove that all the Bass numbers of local cohomology modules are finite for all $j \in{\mathbb Z}$ provided that the residue field is separable over $k$. We also prove that the set of associated prime ideals of those is a finite set under the same hypothesis. Furthermore, we shall discuss finiteness properties of local cohomology modules over regular local rings.

Article information

Source
Illinois J. Math., Volume 52, Number 3 (2008), 727-744.

Dates
First available in Project Euclid: 1 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1254403711

Digital Object Identifier
doi:10.1215/ijm/1254403711

Mathematical Reviews number (MathSciNet)
MR2546004

Zentralblatt MATH identifier
1174.13025

Subjects
Primary: 14B15: Local cohomology [See also 13D45, 32C36] 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)

Citation

Kawasaki, Ken-ichiroh. On finiteness properties of local cohomology modules over Cohen–Macaulay local rings. Illinois J. Math. 52 (2008), no. 3, 727--744. doi:10.1215/ijm/1254403711. https://projecteuclid.org/euclid.ijm/1254403711


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