Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 52, Number 3 (2008), 727-744.
On finiteness properties of local cohomology modules over Cohen–Macaulay local rings
Full-text: Open access
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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