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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Published in | Czechoslovak mathematical journal Vol. 72; no. 2; pp. 541 - 558 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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
. |
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ISSN: | 0011-4642 1572-9141 |
DOI: | 10.21136/CMJ.2022.0050-21 |