Deformations of algebraic schemes via Reedy–Palamodov cofibrant resolutions

Let X be a Noetherian separated and finite dimensional scheme over a field K of characteristic zero. The goal of this paper is to study deformations of X over a differential graded local Artin K-algebra by using local Tate–Quillen resolutions, i.e., the algebraic analogous of the Palamodov's resolvent of a complex space. The above goal is achieved by describing the DG-Lie algebra controlling deformation theory of a diagram of differential graded commutative algebras, indexed by a direct Reedy category