nLab
derived Deligne-Mumford stack

Idea

… derived algebraic geometry … higher algebra …generalized scheme…

Definition

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 $𝒢={𝒢}_{\mathrm{et}}(k)$ the étale geometry (for structured (infinity,1)-toposes).

Special cases

A 1-localic derived Deligne-Mumford stack is an ordinary Deligne-Mumford stack. See there for more details.

related concepts

Notice that for generalized schemes the étale geometry (for structured (infinity,1)-toposes) ${𝒢}_{\mathrm{et}}(k)$ is not interchangeable with the Zariski geometry ${𝒢}_{\mathrm{et}}(k)$. Instead ${𝒢}_{\mathrm{Zar}}(k)$-generalized schemes are derived schemes.

References

section 4.3 in

• Jacob Lurie, Structured Spaces