Warnings:
Theorem 2.10 in the preprint is most likely incorrect. This is the reason for the 2nd warning.
There is a possible error in the preprint. Definition 3.7 should be "the localization w.r.t. the surjective quasi-isomorphisms." With this modification, Cor 3.8 is most likely true, and likewise for the remaining assertions in the preprint.
Title: The Derived Category of Sheaves of Commutative DG Rings (Preview)
Authors: Amnon Yekutieli
Publication status: arXiv:1608.04265
Abstract: In this short paper we outline (mostly without proofs) our new approach to the derived category of sheaves of commutative DG rings. The proofs will appear in a subsequent paper.
Among other things, we explain how to form the derived intersection of two closed subschemes inside a given algebraic scheme X, without recourse to simplicial or higher homotopical methods, and without any global assumptions on X.
updated 18 Oct 2022, 13 Feb 2023