Finiteness properties of extension functors of cofinite modules (Q2857007)
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scientific article; zbMATH DE number 6221361
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finiteness properties of extension functors of cofinite modules |
scientific article; zbMATH DE number 6221361 |
Statements
31 October 2013
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arithmetic rank
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cofinite modules
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local cohomology
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minimax modules
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Finiteness properties of extension functors of cofinite modules (English)
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Let \(R\) be a Noetherian ring and \(I\) an ideal. An \(R\)-module \(M\) is said to be \(I\)-cofinite if \(\text{Supp} M \subset V(I)\) and \(\text{Ext}^i(R/I, M)\) are finitely generated for all \(i\). In the present paper, the authors consider the following question: Let \(M\) be an \(I\)-cofinite \(R\)-module. Are the \(R\)-module \(\text{Ext}^i(M, R/I)\) finitely generated for all \(i\)? They provide an affirmative answer if \(\dim M \leq 1\).
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