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arXiv · 1701.07727

Local Homology, Koszul Homology and Serre Classes

Kamran Divaani-Aazar·Hossein Faridian·Massoud Tousi
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Abstract

Given a Serre class $\mathcal{S}$ of modules, we compare the containment of the Koszul homology, Ext modules, Tor modules, local homology, and local cohomology in $\mathcal{S}$ up to a given bound $s \geq 0$. 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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Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi. 2018-04-26. Local Homology, Koszul Homology and Serre Classes. https://arxiv.org/abs/1701.07727

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