| Title:
|
On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals (English) |
| Author:
|
Freitas, Thiago H. |
| Author:
|
Jorge Pérez, Victor H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
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0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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69 |
| Issue:
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2 |
| Year:
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2019 |
| Pages:
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453-470 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathfrak {a}$, $I$, $J$ be ideals of a Noetherian local ring $(R,\mathfrak {m},k)$. Let $M$ and $N$ be finitely generated $R$-modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of $H^t_{I,J}(M)$ and $D(H^t_{I,J}(M))$, where $t$ is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and $D(-):= {\rm Hom}_R(-,E_R(k))$ is the Matlis dual functor. We show that if $R$ is a $d$-dimensional complete Cohen-Macaulay ring and $H^i_{I,J}(R)=0$ for all $i\neq t$, the natural homomorphism $R\rightarrow {\rm Hom}_R(H^t_{I,J}(K_R), H^t_{I,J}(K_R))$ is an isomorphism, where $K_R$ denotes the canonical module of $R$. Also, we discuss the depth and Cohen-Macaulayness of the Matlis dual of the top local cohomology modules with respect to a pair of ideals. (English) |
| Keyword:
|
local cohomology |
| Keyword:
|
Matlis duality |
| Keyword:
|
endomorphism ring |
| MSC:
|
13C14 |
| MSC:
|
13D45 |
| idZBL:
|
Zbl 07088798 |
| idMR:
|
MR3959958 |
| DOI:
|
10.21136/CMJ.2018.0386-17 |
| . |
| Date available:
|
2019-05-24T08:59:52Z |
| Last updated:
|
2021-07-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147738 |
| . |
| Reference:
|
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