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arXiv · 1506.09042

Derived complex analytic geometry I: GAGA theorems

Mauro Porta
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Abstract

In this paper, we expand the foundations of derived complex analytic geometry introduced in [DAG-IX] by J. Lurie. We start by studying the analytification functor and its properties. In particular, we prove that for a derived complex scheme locally almost of finite presentation $X$, the canonical map $X^{\mathrm{an}} \to X$ is flat in the derived sense. Next, we provide a comparison result relating derived complex analytic spaces to geometric stacks. Using these results and building on the previous work arXiv:1412.5166, we prove a derived version of the GAGA theorems. As an application, we prove that the infinitesimal deformation theory of a derived complex analytic moduli problem is governed by a differential graded Lie algebra.

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Mauro Porta. 2015-06-30. Derived complex analytic geometry I: GAGA theorems. https://arxiv.org/abs/1506.09042

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