Local cohomology: Associated primes, artinianness and asymptotic behaviour

Details Local cohomology: Associated primes, artinianness and asymptotic behaviour Local cohomology: Associated primes, artinianness and asymptotic behaviour

2008-07-18

arxiv.org/abs/0807.2967v2

Mathematics

Commutative Algebra

7 pages

Scientific paper

Let $R$ be a noetherian ring, $\fa$ an ideal of $R$, $M$ an $R$--module and $n$ a non-negative integer. In this paper we first will study the finiteness properties of the kernel and the cokernel of the natural map $f:\Ext^n_{R}(R/\fa,M)\lo \Hom_{R}(R/\fa,\lc^{n}_{\fa}(M))$. Then we will get some corollaries about the associated primes and artinianness of local cohomology modules. Finally we will study the asymptotic behaviour of the kernel and the cokernel of this natural map in the graded case.

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