| Title:
|
Contracting endomorphisms and dualizing complexes (English) |
| Author:
|
Nasseh, Saeed |
| Author:
|
Sather-Wagstaff, Sean |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
837-865 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring $R$. Our focus is on homological properties of contracting endomorphisms of $R$, e.g., the Frobenius endomorphism when $R$ contains a field of positive characteristic. For instance, in this case, when $R$ is $F$-finite and $C$ is a semidualizing $R$-complex, we prove that the following conditions are equivalent: (i) $C$ is a dualizing $R$-complex; (ii) $C\sim {\bold R}{\rm Hom}_R(^nR,C)$ for some $n>0$; (iii) ${\rm G}_C\text {\rm -dim} ^nR <\infty $ and $C$ is derived ${\bold R}{\rm Hom}_R(^nR,C)$-reflexive for some $n>0$; and (iv) ${\rm G}_C\text {\rm -dim} ^nR <\infty $ for infinitely many $n>0$. (English) |
| Keyword:
|
Bass classes |
| Keyword:
|
contracting endomorphisms |
| Keyword:
|
dualizing complex |
| Keyword:
|
Frobenius endomorphisms |
| Keyword:
|
${\rm G}_{C}$-dimension |
| Keyword:
|
semidualizing complex |
| MSC:
|
13A35 |
| MSC:
|
13D05 |
| MSC:
|
13D09 |
| idZBL:
|
Zbl 06537696 |
| idMR:
|
MR3407609 |
| DOI:
|
10.1007/s10587-015-0212-3 |
| . |
| Date available:
|
2015-10-04T18:25:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144447 |
| . |
| Reference:
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