| Title:
|
Cofiniteness and finiteness of local cohomology modules over regular local rings (English) |
| Author:
|
A'zami, Jafar |
| Author:
|
Pourreza, Naser |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
733-740 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(R,\mathfrak m)$ be a commutative Noetherian regular local ring of dimension $d$ and $I$ be a proper ideal of $R$ such that ${\rm mAss}_R(R/I)={\rm Assh}_R(I)$. It is shown that the $R$-module $H^{{\rm ht}(I)}_I(R)$ is $I$-cofinite if and only if ${\rm cd}(I,R)={\rm ht}(I)$. Also we present a sufficient condition under which this condition the $R$-module $H^i_I(R)$ is finitely generated if and only if it vanishes. (English) |
| Keyword:
|
cofinite module |
| Keyword:
|
Cohen-Macaulay ring |
| Keyword:
|
Krull dimension |
| Keyword:
|
local cohomology |
| Keyword:
|
regular ring |
| MSC:
|
13D45 |
| MSC:
|
13E05 |
| MSC:
|
14B15 |
| idZBL:
|
Zbl 06770126 |
| idMR:
|
MR3697912 |
| DOI:
|
10.21136/CMJ.2017.0116-16 |
| . |
| Date available:
|
2017-09-01T12:23:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146855 |
| . |
| Reference:
|
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| Reference:
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