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On the finiteness properties of extension and torsion functors of local cohomology modules

Author: Kazem Khashyarmanesh
Journal: Proc. Amer. Math. Soc. 135 (2007), 1319-1327
MSC (2000): Primary 13D45, 13D07
Published electronically: December 27, 2006
MathSciNet review: 2276640
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Abstract: Let $ R$ be a commutative Noetherian ring with non-zero identity, $ \mathfrak{a}$ and $ \mathfrak{b}$ ideals of $ R$ with $ \mathfrak{a} \subseteq \mathfrak{b}$, and $ M$ a finitely generated $ R$-module. In this paper, for fixed integers $ j$ and $ n$, we study the finiteness of $ \operatorname{Ext}^j_R(R/\mathfrak{b},H^n_{\mathfrak{a}}(M))$ and $ Tor_j^R(R/\mathfrak{b},H^n_{\mathfrak{a}}(M))$ in several cases.

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Keywords: Local cohomology modules, extension functor, torsion functor, cofinite modules, associated primes, cohomological dimension, coassociated primes, filter regular sequences.
Received by editor(s): November 2, 2005
Received by editor(s) in revised form: February 2, 2006
Published electronically: December 27, 2006
Additional Notes: The author was partially supported by a grant from the Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran (No. 84130025).
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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