Extension functors of local cohomology modules

2009/03/12 by Aghapournahr, M., Taherizadeh, A. J., Vahidi, A.
#13D07 #13D45 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.2093

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.

Related

• Extension functors of generalized local cohomology modules
• Some results on generalized local cohomology modules
• Cofiniteness with respect to extension of Serre subcategories
• Finiteness of extension functors of local cohomology modules
• On the local cohomology modules deffined by a pair of ideals and serre subcategories