Derived complex analytic geometry II: square-zero extensions

doi:https://doi.org/10.48550/arxiv.1507.06602

Open AccessPreprint10.48550/arxiv.1507.06602

Derived complex analytic geometry II: square-zero extensions

Mauro Porta-2015-07-23-arXiv (Cornell University)

TL;DRAbstract

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.

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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.

Keywords

Zero (linguistics)Square (algebra)Extension (predicate logic)MathematicsAnalytic geometrySpace (punctuation)Pure mathematicsGeometry

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