Finite projective dimension and a question of Jorgensen
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915960956387328 |
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| author | Holanda, Rafael Miranda-Neto, Cleto B. |
| author_facet | Holanda, Rafael Miranda-Neto, Cleto B. |
| contents | This paper studies finite projective dimension of finitely generated modules over a Noetherian local ring, by means of spectral sequence methods related to generalized local cohomology. Our main goal is to address a question raised by D. Jorgensen over fifteen years ago, concerning a prescribed bound (via Ext vanishing) for projective dimension over a complete intersection local ring. We obtain similar results involving other homological dimensions as well. Also we make use of weakly full ideals to derive further criteria for prescribed bound on projective dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24500 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite projective dimension and a question of Jorgensen Holanda, Rafael Miranda-Neto, Cleto B. Commutative Algebra Primary 13D05, 13D07, 13H10, 13C10, Secondary 13C13, 13D02, 13D45 This paper studies finite projective dimension of finitely generated modules over a Noetherian local ring, by means of spectral sequence methods related to generalized local cohomology. Our main goal is to address a question raised by D. Jorgensen over fifteen years ago, concerning a prescribed bound (via Ext vanishing) for projective dimension over a complete intersection local ring. We obtain similar results involving other homological dimensions as well. Also we make use of weakly full ideals to derive further criteria for prescribed bound on projective dimension. |
| title | Finite projective dimension and a question of Jorgensen |
| topic | Commutative Algebra Primary 13D05, 13D07, 13H10, 13C10, Secondary 13C13, 13D02, 13D45 |
| url | https://arxiv.org/abs/2604.24500 |