Regular sequences for triangulated categories
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918139818672128 |
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| author | Kekkou, Antonia Letz, Janina C. Stephan, Marc |
| author_facet | Kekkou, Antonia Letz, Janina C. Stephan, Marc |
| contents | This paper systematically develops a notion of regular sequences in the context of $R$-linear triangulated categories for a graded-commutative ring $R$. The notion has equivalent characterizations involving Koszul objects and local cohomology. The main examples are in the context of the Hochschild cohomology ring or the group cohomology ring acting on derived or stable categories. As applications, lengths of regular sequences provide lower bounds for level and Rouquier dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular sequences for triangulated categories Kekkou, Antonia Letz, Janina C. Stephan, Marc Commutative Algebra Category Theory 18G80 (primary), 13D09, 13D45 This paper systematically develops a notion of regular sequences in the context of $R$-linear triangulated categories for a graded-commutative ring $R$. The notion has equivalent characterizations involving Koszul objects and local cohomology. The main examples are in the context of the Hochschild cohomology ring or the group cohomology ring acting on derived or stable categories. As applications, lengths of regular sequences provide lower bounds for level and Rouquier dimension. |
| title | Regular sequences for triangulated categories |
| topic | Commutative Algebra Category Theory 18G80 (primary), 13D09, 13D45 |
| url | https://arxiv.org/abs/2509.09941 |