Corpus ID: 55217220

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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