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Stable local cohomology
- Source :
- Communications in Algebra. 45:198-226
- Publication Year :
- 2016
- Publisher :
- Informa UK Limited, 2016.
-
Abstract
- Let $R$ be a Gorenstein local ring, $\frak{a}$ an ideal in $R$, and $M$ an $R$-module. The local cohomology of $M$ supported at $\frak{a}$ can be computed by applying the $\frak{a}$-torsion functor to an injective resolution of $M$. Since $R$ is Gorenstein, $M$ has a complete injective resolution, so it is natural to ask what one gets by applying the $\frak{a}$-torsion functor to it. Following this lead, we define stable local cohomology for modules with complete injective resolutions. This gives a functor to the stable category of Gorenstein injective modules. We show that in many ways this behaves like the usual local cohomology functor. Our main result is that when there is only one non-zero local cohomology module, there is a strong connection between that module and the stable local cohomology module; in fact, the latter gives a Gorenstein injective approximation of the former.<br />Comment: 29 pages. Comments are welcome!
- Subjects :
- Pure mathematics
Algebra and Number Theory
Functor
Mathematics::Commutative Algebra
Mathematics::Rings and Algebras
010102 general mathematics
Stable module category
Local cohomology
Mathematics - Commutative Algebra
Commutative Algebra (math.AC)
Mathematics::Algebraic Topology
01 natural sciences
Injective function
Mathematics::K-Theory and Homology
Mathematics::Category Theory
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
0101 mathematics
Connection (algebraic framework)
Resolution (algebra)
Mathematics
Subjects
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 45
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi.dedup.....7d0bc7709dcc04043570f1d295cfe662