Cofiniteness with respect to ideals of dimension one

By Leif Melkersson. 2012

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We prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules. The proof is based on a criterion for cofiniteness with respect to an ideal of dimension one. Namely for such ideals it suffices that the two first Ext-modules in the definition for cofiniteness are finitely generated. This criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fdcbcdb387b2b45c1d224fffd0b6feb262c6d6bf