“School of Mathematics”
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| Paper IPM / M / 15522 |
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| Abstract: | |
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Let \mathfraka be an ideal of a commutative noetherian (not necessarily local) ring R. In the case \cd(\mathfraka,R) ≤ 1, we show that the subcategory
of \mathfraka-cofinite R-modules is abelian. Using this and the technique of way-out functors, we show that if \cd(\mathfraka,R) ≤ 1, or dim(R/\mathfraka) ≤ 1, or dim(R) ≤ 2, then the local cohomology module Hi\mathfraka(X) is \mathfraka-cofinite for every R-complex X with finitely generated
homology modules and every i ∈ \mathbbZ. We further answer Question 1.3 in the three aforementioned cases, and reveal a correlation between Questions 1.1,
1.2, and 1.3.
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