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Cofiniteness of generalized local cohomology modules

Kamran Divaani-Aazar·Reza Sazeedeh
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Abstract

Let $\fa$ denote an ideal of a commutative Noetherian ring $R$ and $M$ and $N$ two finitely generated $R$-modules with $\pd M< \infty$. It is shown that if $\fa$ is principal or $R$ is complete local and $\fa$ a prime ideal with $\dim R/\fa=1$, then the generalized local cohomology module $H^i_{\fa}(M,N)$ is $\fa$-cofinite for all $i \geq 0$. This provides an affirmative answer for the above ideal $\fa$ to a question proposed in [{\bf 13}].

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Kamran Divaani-Aazar, Reza Sazeedeh. 2004-08-12. Cofiniteness of generalized local cohomology modules. https://arxiv.org/abs/math/0408163

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