Quasi-smooth derived schemes and perfect obstruction theories

A very nice feature of quasi-smooth derived schemes (in the sense of Toen-Vezzosi and Lurie) is that they induce a  1-perfect obstruction theory on the underlying scheme. This gives rise to a virtual fundamental class on the underlying scheme. I will discuss in detail how this obstruction theory is induced. This requires reviewing some facts about the Postnikov decomposition and the cotangent complex of simplicial algebras.