| Title:
|
Matlis reflexive and generalized local cohomology modules (English) |
| Author:
|
Mafi, Amir |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
1095-1102 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(R,\mathfrak m )$ be a complete local ring, $\mathfrak a $ an ideal of $R$ and $N$ and $L$ two Matlis reflexive $R$-modules with $\mathop{{\rm Supp}} (L)\subseteq V(\mathfrak a )$. We prove that if $M$ is a finitely generated $R$-module, then $\mathop{{\rm Ext}}\nolimits_R^i(L,H_{\mathfrak a }^j(M,N))$ is Matlis reflexive for all $i$ and $j$ in the following cases: (a) $\mathop{{\rm dim}} R/{\mathfrak a }=1$; (b) $\mathop{{\rm cd}} (\mathfrak a )=1$; where $\mathop{{\rm cd}} $ is the cohomological dimension of $\mathfrak a $ in $R$; (c) $\mathop{{\rm dim}} R\leq 2$. In these cases we also prove that the Bass numbers of $H_{\mathfrak a }^j(M,N)$ are finite. (English) |
| Keyword:
|
Bass numbers |
| Keyword:
|
generalized local cohomology modules |
| Keyword:
|
Matlis reflexive |
| MSC:
|
13D07 |
| MSC:
|
13D45 |
| MSC:
|
13E99 |
| idZBL:
|
Zbl 1224.13016 |
| idMR:
|
MR2563580 |
| . |
| Date available:
|
2010-07-20T16:04:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140539 |
| . |
| Reference:
|
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