G-levels of perfect complexes
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911565993738240 |
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| author | Christensen, Lars Winther Kekkou, Antonia Lyle, Justin Nason, Zachary Levins, Andrew J. Soto |
| author_facet | Christensen, Lars Winther Kekkou, Antonia Lyle, Justin Nason, Zachary Levins, Andrew J. Soto |
| contents | We prove that a commutative noetherian ring $R$ is Gorenstein of dimension at most $d$ if $d+1$ is an upper bound on the G-levels of perfect $R$-complexes. For $R$ local, we prove a formula for levels, with respect to injective or Gorenstein injective $R$-modules, of $R$-complexes with finitely generated homology; it mimics Bass' classic formula for injective dimension of finitely generated $R$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | G-levels of perfect complexes Christensen, Lars Winther Kekkou, Antonia Lyle, Justin Nason, Zachary Levins, Andrew J. Soto Commutative Algebra 13D09, 13H10 We prove that a commutative noetherian ring $R$ is Gorenstein of dimension at most $d$ if $d+1$ is an upper bound on the G-levels of perfect $R$-complexes. For $R$ local, we prove a formula for levels, with respect to injective or Gorenstein injective $R$-modules, of $R$-complexes with finitely generated homology; it mimics Bass' classic formula for injective dimension of finitely generated $R$-modules. |
| title | G-levels of perfect complexes |
| topic | Commutative Algebra 13D09, 13H10 |
| url | https://arxiv.org/abs/2507.10486 |