Rocky Mountain Journal of Mathematics

Local homology, Koszul homology and Serre classes

Kamran Divaani-Aazar, Hossein Faridian, and Massoud Tousi

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Abstract

Given a Serre class $\mathcal {S}$ of modules, we compare the containment of Koszul homology, Ext modules, Tor modules, local homology and local cohomology in $\mathcal {S}$ up to a given bound $s \geq 0$. As applications, we give a full characterization of Noetherian local homology modules. Furthermore, we establish a comprehensive vanishing result which readily leads to formerly known descriptions of the numerical invariants' width and depth in terms of Koszul homology, local homology and local cohomology. In addition, we recover a few renowned vanishing criteria scattered throughout the literature.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1841-1869.

Dates
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1543028441

Digital Object Identifier
doi:10.1216/RMJ-2018-48-6-1841

Mathematical Reviews number (MathSciNet)
MR3879305

Zentralblatt MATH identifier
06987228

Subjects
Primary: 13C05: Structure, classification theorems 13D07: Homological functors on modules (Tor, Ext, etc.) 13D45: Local cohomology [See also 14B15]

Keywords
Koszul homology module local cohomology module local homology module Serre class

Citation

Divaani-Aazar, Kamran; Faridian, Hossein; Tousi, Massoud. Local homology, Koszul homology and Serre classes. Rocky Mountain J. Math. 48 (2018), no. 6, 1841--1869. doi:10.1216/RMJ-2018-48-6-1841. https://projecteuclid.org/euclid.rmjm/1543028441


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