A natural map in local cohomology

Moharram Aghapournahr Arak University, P.O. Box 879, Beheshti St, Arak, Iran Leif Melkersson Department of Mathematics, Linköping University

TBD mathscidoc:1701.333174

Arkiv for Matematik, 48, (2), 243-251, 2008.11
Let$R$be a Noetherian ring, $\mathfrak{a}$ an ideal of$R$,$M$an$R$-module and$n$a non-negative integer. In this paper we first study the finiteness properties of the kernel and the cokernel of the natural map $f\colon\operatorname{Ext}^{n}_{R}(R/\mathfrak{a},M)\to \operatorname{Hom}_{R}(R/\mathfrak{a},\mathrm{H}^{n}_{\mathfrak{a}}(M))$ , under some conditions on the previous local cohomology modules. Then we get some corollaries about the associated primes and Artinianness of local cohomology modules. Finally we will study the asymptotic behavior of the kernel and the cokernel of the natural map in the graded case.
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@inproceedings{moharram2008a,
  title={A natural map in local cohomology},
  author={Moharram Aghapournahr, and Leif Melkersson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627871907983},
  booktitle={Arkiv for Matematik},
  volume={48},
  number={2},
  pages={243-251},
  year={2008},
}
Moharram Aghapournahr, and Leif Melkersson. A natural map in local cohomology. 2008. Vol. 48. In Arkiv for Matematik. pp.243-251. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627871907983.
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