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On endomorphism rings of local cohomology

Michael Hellus·Juergen Stueckrad
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Abstract

Let R be a local complete ring. For an R-module M the canonical ring map R\to 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(:= 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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Michael Hellus, Juergen Stueckrad. 2007-03-06. On endomorphism rings of local cohomology. https://arxiv.org/abs/math/0703148

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