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Local Cohomology, Second Edition by R. Y. Sharp, M. P. Brodmann

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11

Local duality

Suppose, temporarily, that (R, images) is local, and that M is a finitely generated R-module. In Theorem 7.1.3, we showed that images(M) is Artinian for all iimageso. When R is complete, Matlis duality (see 10.2.12) provides a very satisfactory correspondence between the category of Artinian R-modules and the category of Noetherian R-modules, and so it is natural to ask, in this situation, which Noetherian R-modules correspond to the local cohomology ...

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