# Infinitesimal and square-zero extensions of simplicial algebras

@article{Porta2013InfinitesimalAS, title={Infinitesimal and square-zero extensions of simplicial algebras}, author={Mauro Porta and G. Vezzosi}, journal={arXiv: Algebraic Geometry}, year={2013} }

We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we show that the Postnikov tower of a simplicial commutative algebra is built out of square-zero extensions. We conclude the notes with two applications: we give connectivity estimates for the cotangent complex and we show how obstructions can be seen as deformations over simplicial rings.

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