Cotorsion pairs and Tor-pairs over commutative noetherian rings
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909379493625856 |
|---|---|
| author | Herbera, Dolors Hrbek, Michal Gros, Giovanna Le |
| author_facet | Herbera, Dolors Hrbek, Michal Gros, Giovanna Le |
| contents | For a commutative noetherian ring $R$, we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of the ring. Each such function gives rise to a system of local depth conditions which describes the left-hand class in the corresponding cotorsion pair. Furthermore, we show that these cotorsion pairs correspond by explicit duality to hereditary Tor-pairs generated by modules of finite flat dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cotorsion pairs and Tor-pairs over commutative noetherian rings Herbera, Dolors Hrbek, Michal Gros, Giovanna Le Commutative Algebra Rings and Algebras 13D07, 13C15, 13E05 (Prymary) 13C11, 16E30 (Secondary) For a commutative noetherian ring $R$, we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is done in terms of integer-valued functions on the spectrum of the ring. Each such function gives rise to a system of local depth conditions which describes the left-hand class in the corresponding cotorsion pair. Furthermore, we show that these cotorsion pairs correspond by explicit duality to hereditary Tor-pairs generated by modules of finite flat dimension. |
| title | Cotorsion pairs and Tor-pairs over commutative noetherian rings |
| topic | Commutative Algebra Rings and Algebras 13D07, 13C15, 13E05 (Prymary) 13C11, 16E30 (Secondary) |
| url | https://arxiv.org/abs/2411.04514 |