On endomorphism rings of local cohomology

Details On endomorphism rings of local cohomology On endomorphism rings of local cohomology

2007-03-06

arxiv.org/abs/math/0703148v1

Mathematics

Commutative Algebra

10 pages

Scientific paper

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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