On Koszul–Tate resolutions and Sullivan models
Volume 531 / 2018
Dissertationes Mathematicae 531 (2018), 1-71
MSC: Primary 18G55; Secondary 16E45.
DOI: 10.4064/dm779-1-2018
Published online: 23 May 2018
Abstract
We report on Koszul–Tate resolutions in algebra, mathematical physics, cohomological analysis of PDEs, and 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.
