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Derived analytic geometry: Derived Kähler space and Hodge theory

2025/06/24 by Haibara, Eita
#14A30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.19629

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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