Journal of Mathematics of Kyoto University

On the annihilation of local cohomology modules

Javad Asadollahi and Shokrollah Salarian

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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

J. Math. Kyoto Univ., Volume 46, Number 2 (2006), 357-365.

First available in Project Euclid: 14 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13D05: Homological dimension 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]


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.

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