Vanishing of DHKK complexities for singularity categories and generation of syzygy modules
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910933675147264 |
|---|---|
| author | Araya, Tokuji Iima, Kei-ichiro Takahashi, Ryo |
| author_facet | Araya, Tokuji Iima, Kei-ichiro Takahashi, Ryo |
| contents | Let R be a commutative noetherian ring. In this paper, we study, for the singularity category of R, the vanishing of the complexity $δ_t(X,Y)$ in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich. We prove that the set of real numbers t such that $δ_t(X,Y)$ does not vanish is bounded in various cases. We do it by building the high syzygy modules and maximal Cohen-Macaulay modules out of a single module only by taking direct summands and extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15475 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vanishing of DHKK complexities for singularity categories and generation of syzygy modules Araya, Tokuji Iima, Kei-ichiro Takahashi, Ryo Commutative Algebra Representation Theory 13D09, 13C60 Let R be a commutative noetherian ring. In this paper, we study, for the singularity category of R, the vanishing of the complexity $δ_t(X,Y)$ in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich. We prove that the set of real numbers t such that $δ_t(X,Y)$ does not vanish is bounded in various cases. We do it by building the high syzygy modules and maximal Cohen-Macaulay modules out of a single module only by taking direct summands and extensions. |
| title | Vanishing of DHKK complexities for singularity categories and generation of syzygy modules |
| topic | Commutative Algebra Representation Theory 13D09, 13C60 |
| url | https://arxiv.org/abs/2310.15475 |