Local cohomology, cofiniteness and homological functors of modules

Let I be an ideal of a commutative Noetherian ring R . It is shown that the R -modules H I j ( M ) are I -cofinite for all finitely generated R -modules M and all j ∈ ℕ 0 if and only if the R -modules Ext R i ( N ,H I j ( M )) and Tor i R ( N, H I j ( M )) are I -cofinite for all finitely generated...

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Bibliographic Details
Published inCzechoslovak mathematical journal Vol. 72; no. 2; pp. 541 - 558
Main Author Bahmanpour, Kamal
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2022
Springer Nature B.V
Subjects
Analysis
Convex and Discrete Geometry
Homology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Modules
Ordinary Differential Equations
local cohomology
13E05
cohomological dimension
cofinite module
14B15
Noetherian ring
13D45
ideal transform
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Summary:Let I be an ideal of a commutative Noetherian ring R . It is shown that the R -modules H I j ( M ) are I -cofinite for all finitely generated R -modules M and all j ∈ ℕ 0 if and only if the R -modules Ext R i ( N ,H I j ( M )) and Tor i R ( N, H I j ( M )) are I -cofinite for all finitely generated R -modules M, N and all integers i, j ∈ ℕ 0 .
ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2022.0050-21