Quasi-Isomorphisms of Commutative DG Rings and Divided Power Structures

Author:

Amnon Yekutieli

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC), K-Theory and Homology (math.KT)

journal:

date:

2023-05-09 16:00:00

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.

PDF: Quasi-Isomorphisms of Commutative DG Rings and Divided Power Structures.pdf