On Koszul–Tate resolutions and Sullivan models

Abstract

We report on Koszul-Tate resolutions in Algebra, in Mathematical Physics, in Cohomological Analysis of PDE-s, and in Homotopy Theory. Further, we define an abstract Koszul-Tate resolution in the frame of $\mathcal{D}$-Geometry, i.e., geometry over differential operators. We prove Comparison Theorems for these resolutions, thus providing a dictionary between the different fields. Eventually, we show that all these resolutions are of the new $\mathcal{D}$-geometric type.