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Paper   IPM / M / 15524
School of Mathematics
  Title:   Local homology, Koszul homology and Serre classes
  Author(s):  Kamran Divaani-Aazar (Joint with H. Faridian and M. Tousi)
  Status:   To Appear
  Journal: Rocky Mountain J. Math.
  Supported by:  IPM
Given a Serre class S of modules, we compare the containment of the Koszul homology, Ext modules, Tor modules, local homology, and local cohomology in S up to a given bound s ≥ 0. As some applications, we give a full characterization of noetherian local homology modules. Further, we establish a comprehensive vanishing result which readily leads to the formerly known descriptions of the numerical invariants width and depth in terms of Koszul homology, local homology, and local cohomology. Also, we immediately recover a few renowned vanishing criteria scattered about the literature.

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