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arXiv · 2506.19629

Derived analytic geometry: Derived Kähler space and Hodge theory

Eita Haibara
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Abstract

We introduce higher analytic geometry, a novel framework extending Lurie's derived complex analytic spaces. This theory generalizes classical complex analytic geometry, enabling the study of derived Kähler spaces with non-trivial higher homotopy groups. We develop derived de Rham and Dolbeault cohomologies, yielding a Hodge decomposition for compact derived Kähler spaces, and establish a derived Stokes' theorem, unifying classical results with homotopical structures.

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Eita Haibara. 2025-06-30. Derived analytic geometry: Derived Kähler space and Hodge theory. https://arxiv.org/abs/2506.19629

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