The derived depth formula for modules of finite quasi-projective dimension
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910200218255360 |
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| author | Ferraro, Luigi Lyle, Justin |
| author_facet | Ferraro, Luigi Lyle, Justin |
| contents | Let $R$ be a commutative Noetherian local ring. We prove a variety of new formulae for modules of finite quasi-projective or finite quasi-injective dimension. These include the Derived Depth Formula, itself an extension of Auslander famous depth formula, a variation of the Derived Depth Formula for width, an extended version of Ischebeck's Formula, and a Dependency formula in the vein of Jorgensen. Several special cases of our main results are new even under stronger assumptions on the vanishing of various complete intersection dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The derived depth formula for modules of finite quasi-projective dimension Ferraro, Luigi Lyle, Justin Commutative Algebra 13D02, 13D05, 13D09 Let $R$ be a commutative Noetherian local ring. We prove a variety of new formulae for modules of finite quasi-projective or finite quasi-injective dimension. These include the Derived Depth Formula, itself an extension of Auslander famous depth formula, a variation of the Derived Depth Formula for width, an extended version of Ischebeck's Formula, and a Dependency formula in the vein of Jorgensen. Several special cases of our main results are new even under stronger assumptions on the vanishing of various complete intersection dimensions. |
| title | The derived depth formula for modules of finite quasi-projective dimension |
| topic | Commutative Algebra 13D02, 13D05, 13D09 |
| url | https://arxiv.org/abs/2605.07004 |