β¦ derived algebraic geometry β¦ higher algebra β¦generalized schemeβ¦
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 Γ©tale geometry . Instead -generalized schemes are derived Deligne-Mumford stacks.
section 4.2 in