Quillen-Suslin Theorem for connected cochain DG algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914045532045312 |
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| author | Mao, Xuefeng Zhu, Biyan |
| author_facet | Mao, Xuefeng Zhu, Biyan |
| contents | Let $\mathscr{A}$ be a connected cochain DG algebra and $P$ a DG $\mathscr{A}$-module such that its underlying graded module $P^{\#}$ is a finitely generated $\mathscr{A}^{\#}$-module. We show that $P$ is semi-free if it is semi-projective and it is categorically free if it is categorically projective. It can be considered as a generalization of the well-known Quillen-Suslin Theorem in DG context. As an application, we show that the ghost length and the cone length of a compact DG module coincide. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01120 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quillen-Suslin Theorem for connected cochain DG algebras Mao, Xuefeng Zhu, Biyan Rings and Algebras 16E10, 16E45, 16W50, 16E65 Let $\mathscr{A}$ be a connected cochain DG algebra and $P$ a DG $\mathscr{A}$-module such that its underlying graded module $P^{\#}$ is a finitely generated $\mathscr{A}^{\#}$-module. We show that $P$ is semi-free if it is semi-projective and it is categorically free if it is categorically projective. It can be considered as a generalization of the well-known Quillen-Suslin Theorem in DG context. As an application, we show that the ghost length and the cone length of a compact DG module coincide. |
| title | Quillen-Suslin Theorem for connected cochain DG algebras |
| topic | Rings and Algebras 16E10, 16E45, 16W50, 16E65 |
| url | https://arxiv.org/abs/2509.01120 |