## Journal of Mathematics of Kyoto University

### On the annihilation of local cohomology modules

#### 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

https://projecteuclid.org/euclid.kjm/1250281781

Digital Object Identifier
doi:10.1215/kjm/1250281781

Mathematical Reviews number (MathSciNet)
MR2284348

Zentralblatt MATH identifier
1112.13018

#### 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