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On Koszul-Tate resolutions and Sullivan models. (English) Zbl 1474.18037

Summary: 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.

MSC:

18N40 Homotopical algebra, Quillen model categories, derivators
16E45 Differential graded algebras and applications (associative algebraic aspects)
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