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.
Jacob Lurie, Closed Immersions (DAG IX).
Mauro Porta, Tony Yue Yu?, Higher analytic stacks and GAGA theorems, Derived non-archimedean analytic spaces, Selecta Math. New Ser. 24, 609-665 (2018) arXiv:1601.00859 doi
Mauro Porta, Tony Yue Yu?, Derived non-archimedean analytic spaces, Selecta Math. New Ser. 24, 609-665 (2018) arXiv:1601.00859 doi
Mauro Porta, Derived complex analytic geometry I: GAGA theorems, arXiv:1506.09042
Mauro Porta, Derived complex analytic geometry II: square-zero extensions, arXiv:1507.06602
Frédéric Paugam, Overconvergent global analytic geometry, arXiv:1410.7971.
Last revised on June 20, 2023 at 11:20:05. See the history of this page for a list of all contributions to it.