On the finiteness of associated primes of local cohomology modules

Quy, Pham

doi:10.1090/S0002-9939-10-10235-4

On the finiteness of associated primes of local cohomology modules
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by Pham Hung Quy PDF

Proc. Amer. Math. Soc. 138 (2010), 1965-1968 Request permission

Abstract:

Let $R$ be a Noetherian ring, $\mathfrak a$ be an ideal of $R$ and $M$ be a finitely generated $R$-module. The aim of this paper is to show that if $t$ is the least integer such that neither $H^t_{\mathfrak a}(M)$ nor $\mathrm {supp}(H^t_{\mathfrak a}(M))$ is non-finite, then $H^t_{\mathfrak a}(M)$ has finitely many associated primes. This combines the main results of Brodmann and Faghani and independently of Khashyarmanesh and Salarian.

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