… derived algebraic geometry … higher algebra …generalized scheme…
Let k be a commutative ring.
A derived Deligne-Mumford stack (over k) is a generalized scheme in the sense of locally affine 𝒢-structured (infinity,1)-topos for 𝒢=𝒢 et(k) 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.
Notice that for generalized schemes the étale geometry (for structured (infinity,1)-toposes) 𝒢 et(k) is not interchangeable with the Zariski geometry 𝒢 et(k). Instead 𝒢 Zar(k)-generalized schemes are derived schemes.
section 4.3 in