higher geometry / derived geometry
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… derived algebraic geometry … higher algebra …generalized scheme…
Let be a commutative ring.
A derived scheme (over ) is a generalized scheme in the sense of locally affine -structured (infinity,1)-topos for the Zariski geometry (for structured (infinity,1)-toposes).
A 0-trucated and 0-localic derived scheme is precisely an ordinary scheme.
More precisely:
Let be the full subcategory of all derived schemes on the 0-trucated and 0-localic ones. This is canonically equivalent to the ordinary category of schemes over :
For more comments on this see also
Notice that for generalized schemes the Zariski geometry (for structured (infinity,1)-toposes) is not interchangeable with the étale (∞,1)-site . Instead -generalized schemes are derived Deligne-Mumford stacks.
section 4.2 in
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