Derived complex analytic geometry II: square-zero extensions

Abstract

We continue the explorations of derived \canal geometry started in [DAG-IX] and in http://arxiv.org/abs/1506.09042. We describe the category of ${\mathcal{O}}_X$-modules over a derived complex analytic space $X$ as the stabilization of a suitable category of analytic algebras over ${\mathcal{O}}_X$. Finally, we apply this description to introduce the notion of analytic square-zero extension and prove a fundamental structure theorem for them.

Comments are very welcome. 57 pages

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