Illinois Journal of Mathematics

On injective resolutions of local cohomology modules

Tony J. Puthenpurakal

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Abstract

Let $R=K[X_{1},\ldots,X_{n}]$ where $K$ is a field of characteristic zero. Let $I$ be an ideal in $R$ and let $M=H^{i}_{I}(R)$ be the $i$th-local cohomology module of $R$ with respect to $I$. Let $c=\operatorname{injdim} M$. We prove that if $P$ is a prime ideal in $R$ with Bass number $\mu_{c}(P,M)>0$ then $P$ is a maximal ideal in $R$.

Article information

Source
Illinois J. Math., Volume 58, Number 3 (2014), 709-718.

Dates
Received: 25 February 2014
Revised: 15 April 2015
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1441790386

Digital Object Identifier
doi:10.1215/ijm/1441790386

Mathematical Reviews number (MathSciNet)
MR3395959

Zentralblatt MATH identifier
1330.13029

Subjects
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13D02: Syzygies, resolutions, complexes 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Puthenpurakal, Tony J. On injective resolutions of local cohomology modules. Illinois J. Math. 58 (2014), no. 3, 709--718. doi:10.1215/ijm/1441790386. https://projecteuclid.org/euclid.ijm/1441790386


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References

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