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Paper   IPM / M / 15522
School of Mathematics
  Title:   A New outlook on cofiniteness
  Author(s):  Kamran Divaani-Aazar (Joint with H. Faridian and M. Tousi)
  Status:   To Appear
  Journal: Kyoto J. Math.
  Supported by:  IPM
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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