Quillen–Suslin Theorem for Connected Cochain DG Algebras
Abstract
Let A be a connected cochain differential graded algebra and P a finitely generated differential graded 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 differential graded context. As an application, we show that the ghost length and the cone length of a compact differential graded module coincide.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Rings
Modules
and Algebras
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 12
- Pages
- 2215–2215
- Publication date
- 20 June 2026
- Language
- EN