A filtered Maurer-Cartan theory and minimal L_infty model control splittings of supermanifolds, with the Atiyah class containing the full Green obstruction tower.
Lurie,Derived Algebraic Geometry V: Structured Spaces, preprint
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Formal moduli and the splitting theory of supermanifolds
A filtered Maurer-Cartan theory and minimal L_infty model control splittings of supermanifolds, with the Atiyah class containing the full Green obstruction tower.