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arXiv · 2509.01120

Quillen-Suslin Theorem for connected cochain DG algebras

Xuefeng Mao·Biyan Zhu
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Abstract

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.

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Xuefeng Mao, Biyan Zhu. 2025-09-01. Quillen-Suslin Theorem for connected cochain DG algebras. https://arxiv.org/abs/2509.01120

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