Cofiniteness of generalized local cohomology modules

Kamran Divaani-Aazar¹ ; Reza Sazeedeh²

¹ Department of Mathematics Az-Zahra University, Vanak Tehran 19834, Iran and Institute for Studies in Theoretical Physics and Mathematics P.O. Box 19395-5746, Tehran, Iran
² Department of Mathematics Uromeiyeh University Uromeiyeh, Iran and Institute of Mathematics University for Teacher Education 599 Taleghani Avenue Tehran 15614, Iran

Colloquium Mathematicum, Tome 99 (2004) no. 2, pp. 283-290

Résumé

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}].

Détail

DOI : 10.4064/cm99-2-12

Keywords: mathfrak denote ideal commutative noetherian ring and finitely generated r modules mathop infty shown either mathfrak principal complete local mathfrak prime ideal dim mathfrak generalized local cohomology module mathfrak mathfrak a cofinite geq provides affirmative answer question proposed