Illinois Journal of Mathematics

On injective resolutions of local cohomology modules

Tony J. Puthenpurakal

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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  • V. Bavula, Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic, Represent. Theory 13 (2009), 182–227.
  • W. Bruns and J. Herzog, Cohen–Macaulay rings, revised ed., Cambridge Stud. Adv. Math., vol. 39, Cambridge University Press, Cambridge, 1998.
  • C. Huneke and R. Sharp, Bass numbers of local cohomology modules, Trans. Amer. Math. Soc. 339 (1993), 765–779.
  • G. Lyubeznik, Finiteness properties of local cohomology modules (an application of D-modules to commutative algebra), Invent. Math. 113 (1993), 41–55.
  • G. Lyubeznik, F-modules: Applications to local cohomology and D-modules in characteristic $p>0$, J. Reine Angew. Math. 491 (1997), 65–130.
  • G. Lyubeznik, A characteristic-free proof of a basic result on D-modules, J. Pure Appl. Algebra 215 (2011), no. 8, 2019–2023.
  • H. Matsumura, Commutative ring theory, 2nd ed., Cambridge Stud. Adv. Math., vol. 8, Cambridge University Press, Cambridge, 1989.