Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 46, Number 2 (2006), 357-365.
On the annihilation of local cohomology modules
Javad Asadollahi and Shokrollah Salarian
Abstract
Let $R$ be a (not necessary finite dimensional) commutative noetherian ring and let $C$ be a semi-dualizing module over $R$. There is a generalized Gorenstein dimension with respect to $C$, namely $\mathrm{G}_{C}$-dimension, sharing the nice properties of Auslander’s Gorenstein dimension. In this paper, we establish the Faltings’ Annihilator Theorem and it’s uniform version (in the sense of Raghavan) for local cohomology modules over the class of finitely generated $R$-modules of finite $\mathrm{G}_{C}$-dimension, provided $R$ is Cohen-Macaulay. Our version contains variations of results already known on the Annihilator Theorem.
Article information
Source
J. Math. Kyoto Univ., Volume 46, Number 2 (2006), 357-365.
Dates
First available in Project Euclid: 14 August 2009
Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281781
Digital Object Identifier
doi:10.1215/kjm/1250281781
Mathematical Reviews number (MathSciNet)
MR2284348
Zentralblatt MATH identifier
1112.13018
Subjects
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13D05: Homological dimension 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Citation
Asadollahi, Javad; Salarian, Shokrollah. On the annihilation of local cohomology modules. J. Math. Kyoto Univ. 46 (2006), no. 2, 357--365. doi:10.1215/kjm/1250281781. https://projecteuclid.org/euclid.kjm/1250281781
