higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
symmetric monoidal (∞,1)-category of spectra
This entry provides hyperlinks for central keywords of the text
Structured Spaces
which develops the generalization of the notion of a ringed topos from topos theory to (∞,1)-topos theory and formulates basic notions of geometry in this context (“higher geometry”).
Precursor in 1-category theory include
Monique Hakim, Topos annelés et schémas relatifs, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 64, Springer, Berlin, New York (1972) (doi:10.1007/978-3-662-59155-0)
The theory is general, but the focus of the examples and applications is on derived algebraic geometry/E-∞ geometry.
Apparently a version of this is to eventually appear as:
A survey is at A Survey of Elliptic Cohomology - the derived moduli stack of derived elliptic curves in the section notions of space.
Last revised on October 31, 2020 at 12:23:30. See the history of this page for a list of all contributions to it.