Cofiniteness of generalized local cohomology modules
Volume 99 / 2004
Colloquium Mathematicum 99 (2004), 283-290
MSC: 13D45, 14B15.
DOI: 10.4064/cm99-2-12
Abstract
Let ${\mathfrak a}$ denote an ideal of a commutative Noetherian ring $R$, and $M$ and $N$ two finitely generated $R$-modules with $\mathop{\rm pd} M< \infty$. It is shown that if either ${\mathfrak a}$ is principal, or $R$ is complete local and ${\mathfrak a}$ is a prime ideal with $\dim R/{\mathfrak a}=1$, then the generalized local cohomology module $H^i_{{\mathfrak a}}(M,N)$ is $\mathfrak a$-cofinite for all $i \geq 0$. This provides an affirmative answer to a question proposed in [{13}].
