Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension functors of local cohomology modules   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.

22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci