Tilting complexes and codimension functions over commutative noetherian rings
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908579364077568 |
|---|---|
| author | Hrbek, Michal Nakamura, Tsutomu Šťovíček, Jan |
| author_facet | Hrbek, Michal Nakamura, Tsutomu Šťovíček, Jan |
| contents | In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice" condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from a codimension function on the spectrum. In the absence of a dualizing complex, the situation is more delicate and the tilting property is closely related to the condition that the ring is a homomorphic image of a Cohen-Macaulay ring. We also provide dual versions of our results in the cosilting case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01309 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tilting complexes and codimension functions over commutative noetherian rings Hrbek, Michal Nakamura, Tsutomu Šťovíček, Jan Commutative Algebra Rings and Algebras Representation Theory 13D09 (Primary) 13D45, 13H10, 18G80 (Secondary) In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice" condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from a codimension function on the spectrum. In the absence of a dualizing complex, the situation is more delicate and the tilting property is closely related to the condition that the ring is a homomorphic image of a Cohen-Macaulay ring. We also provide dual versions of our results in the cosilting case. |
| title | Tilting complexes and codimension functions over commutative noetherian rings |
| topic | Commutative Algebra Rings and Algebras Representation Theory 13D09 (Primary) 13D45, 13H10, 18G80 (Secondary) |
| url | https://arxiv.org/abs/2207.01309 |