nLab higher complex analytic geometry

Idea

The higher geometry version of complex analytic geometry, for instance (petit) with geometry (for structured ((∞,1)-toposes) being the site of Stein manifolds or (gros) complex analytic ∞-groupoids.

Related concepts

• GAGA

• higher differential geometry

• higher structures

References

• Jacob Lurie, section 4.4. of Structured Spaces

• Jacob Lurie, sections 11 and 12 of Closed Immersions

• Finnur Larusson, Excision for simplicial sheaves on the Stein site and Gromov’s Oka principle (arXiv:math/0101103)

• Michael Hopkins, Gereon Quick, Hodge filtered complex bordism (arXiv:1212.2173)

• Differential cohomology is Cohesive homotopy theory

  talk notes on how cohesion is a faithful axiomatization of generalized differential cohomology including differential moduli stack constructions such as that of intermediate Jacobians in higher complex analytic geometry.

• Mauro Porta, Tony Yue Yu?, Higher analytic stacks and GAGA theorems, arXiv:1412.5166.

• Eita Haibara?, Derived analytic geometry: Derived Kähler space and Hodge theory, arXiv:2506.19629 .