derived analytic geometry



Derived analytic geometry is the study of derived analogs of analytic spaces in various context, such as complex analytic geometry, non-archimedean analytic geometry and global analytic geometry.

The main motivation for the introduction of derived analytic spaces is to have a proper functorial setting for deformation theory and the cotangent complex in analytic geometry, to prove an Artin/Lurie representability theorem, that characterizes Artin stacks among higher derived stacks.

One also gets, using these methods, a derived construction of the Chern character and an analytic version of derived de Rham cohomology.

Derived analytic methods may also be useful to study intersection theory and virtual fundamental classes on some analytic moduli spaces.