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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18708 |
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| _version_ | 1866913568824229888 |
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| author | Frank, Jonas Schulze, Mathias |
| author_facet | Frank, Jonas Schulze, Mathias |
| contents | Buchweitz related the singularity category of a (strongly) Gorenstein ring and the stable category of maximal Cohen-Macaulay modules by a triangle equivalence. We phrase his result in a relative categorical setting based on N-complexes instead of classical 2-complexes. The role of Cohen-Macaulay modules is played by chains of monics in a Frobenius subcategory of an exact category. As a byproduct, we provide foundational results on derived categories of N-complexes over exact categories known from the Abelian case or for 2-complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stabilized bounded N-derived category of an exact category Frank, Jonas Schulze, Mathias Category Theory Commutative Algebra 18G50, 18G80 (Primary) 16E65, 18G35, 18G65 (Secondary) Buchweitz related the singularity category of a (strongly) Gorenstein ring and the stable category of maximal Cohen-Macaulay modules by a triangle equivalence. We phrase his result in a relative categorical setting based on N-complexes instead of classical 2-complexes. The role of Cohen-Macaulay modules is played by chains of monics in a Frobenius subcategory of an exact category. As a byproduct, we provide foundational results on derived categories of N-complexes over exact categories known from the Abelian case or for 2-complexes. |
| title | The stabilized bounded N-derived category of an exact category |
| topic | Category Theory Commutative Algebra 18G50, 18G80 (Primary) 16E65, 18G35, 18G65 (Secondary) |
| url | https://arxiv.org/abs/2407.18708 |