… derived algebraic geometry … higher algebra …generalized scheme…
…E-∞ scheme, locally representable structured (∞,1)-topos
Let be a commutative ring.
A derived Deligne-Mumford stack (over ) is a generalized scheme in the sense of locally affine -structured (infinity,1)-topos for the étale geometry (for structured (infinity,1)-toposes).
A 1-localic derived Deligne-Mumford stack is an ordinary Deligne-Mumford stack. See there for more details.
spectral Deligne-Mumford stack is quasi-compact, quasi-separated E-∞ algebraic space precisely if it admits a scallop decomposition.
The (∞,1)-presheaves on E-∞ rings which are represented by spectral Deligne-Mumford stacks are described by the Artin-Lurie representability theorem.
Notice that for generalized schemes the étale geometry (for structured (infinity,1)-toposes) is not interchangeable with the Zariski geometry . Instead -generalized schemes are derived schemes.
In the context of E-infinity geometry (spectral Deligne-Mumford stacks):
Last revised on May 22, 2014 at 09:38:20. See the history of this page for a list of all contributions to it.