Quasi-Isomorphisms of Commutative DG Rings and Divided Power Structures

Abstract

We prove that a quasi-isomorphism $f:A\to B$ between commutative DG rings, where $B$ admits a divided power structure, can be factored as $f=\tilde{f}\circ e$, where $e:A\to \tilde{B}$ is a split injective quasi-isomorphism, and $\tilde{f}:\tilde{B}\to B$ is a surjective quasi-isomorphism. This result is used in our work on a DG approach to the cotangent complex, and our work on the derived category of commutative DG rings.

this version: 7 pages, minor improvements