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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.11105 |
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| _version_ | 1866917504790560768 |
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| author | Brown, Michael K. Lyle, Justin |
| author_facet | Brown, Michael K. Lyle, Justin |
| contents | A theorem of Gulliksen states that a local ring is a complete intersection if and only if the Betti numbers of its finitely generated modules grow polynomially. We prove a derived version of Gulliksen's Theorem. More precisely, we prove a structure theorem for dg-algebras whose modules exhibit polynomial Betti growth. As a key ingredient in the proof, we establish the existence and uniqueness of minimal models and acyclic closures of morphisms of dg-algebras in a broader setting than was previously known. We also extend to dg-algebras a theorem of Halperin on the vanishing of deviations of local rings, recovering Gulliksen's Theorem as an immediate consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11105 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derived complete intersections and polynomial growth of Betti numbers over dg-algebras Brown, Michael K. Lyle, Justin Commutative Algebra 13D02, 14F08 A theorem of Gulliksen states that a local ring is a complete intersection if and only if the Betti numbers of its finitely generated modules grow polynomially. We prove a derived version of Gulliksen's Theorem. More precisely, we prove a structure theorem for dg-algebras whose modules exhibit polynomial Betti growth. As a key ingredient in the proof, we establish the existence and uniqueness of minimal models and acyclic closures of morphisms of dg-algebras in a broader setting than was previously known. We also extend to dg-algebras a theorem of Halperin on the vanishing of deviations of local rings, recovering Gulliksen's Theorem as an immediate consequence. |
| title | Derived complete intersections and polynomial growth of Betti numbers over dg-algebras |
| topic | Commutative Algebra 13D02, 14F08 |
| url | https://arxiv.org/abs/2605.11105 |