Extension functors of local cohomology modules

M. Aghapournahr; A. J. Taherizadeh; A. Vahidi

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arXiv · 0903.2093

Extension functors of local cohomology modules

M. Aghapournahr·A. J. Taherizadeh·A. Vahidi

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Abstract

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, and $X$ an $R$--module. In this paper, for fixed integers $s, t$ and a finite $\fa$--torsion $R$--module $N$, we first study the membership of $\Ext^{s+t}_{R}(N, X)$ and $\Ext^{s}_{R}(N, H^{t}_{\fa}(X))$ in Serre subcategories of the category of $R$--modules. Then we present some conditions which ensure the existence of an isomorphism between them. Finally, we introduce the concept of Serre cofiniteness as a generalization of cofiniteness and study this property for certain local cohomology modules.

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BibTeX RIS

M. Aghapournahr, A. J. Taherizadeh, A. Vahidi. 2009-03-12. Extension functors of local cohomology modules. https://arxiv.org/abs/0903.2093

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