On endomorphism rings of local cohomology modules

Hellus, M.; Stückrad, J.

doi:10.1090/S0002-9939-08-09240-X

On endomorphism rings of local cohomology modules
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by M. Hellus and J. Stückrad PDF

Proc. Amer. Math. Soc. 136 (2008), 2333-2341 Request permission

Abstract:

Let $R$ be a local complete ring. For an $R$-module $M$ the canonical ring map $R\to \mathrm {End}_R(M)$ is in general neither injective nor surjective; we show that it is bijective for every local cohomology module $M:=H^h_I(R)$ if $H^l_I(R)=0$ for every $l\neq h$ $(=\mathrm {height} (I))$ ($I$ an ideal of $R$); furthermore the same holds for the Matlis dual of such a module. As an application we prove new criteria for an ideal to be a set-theoretic complete intersection.

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