A natural map in local cohomology (Q711472)

In the paper under review the authors study the finiteness properties of the kernel and cokernel of the natural map from some Ext-modules to the \(\mathfrak a\)-annihalator of the local cohomology module and then give some results on associated primes and Artinian property of some local cohomology modules. Let \(R\) be a Noetherian ring, \(\mathfrak a\) an ideal of \(R\), \(M\) an \(R\)-module and \(n\) be a non-negative integer. Let \(f:\text{Ext}^n_R(R/\mathfrak a,M)\to\Hom_R(R/\mathfrak a,H^n_{\mathfrak a}(M))\) be the natural map. The authors, under some conditions on the previous local cohomology modules, study some properties of \(\text{Ker\,}f\) and \(\text{Coker\,}f\). Then, in the graded setting, they get some results on asymptotic behavior of \(\text{Ker\,}f\) and \(\text{Coker\,}f\).