Differential graded scheme

In algebraic geometry, a derived scheme is a pair ${\displaystyle (X,{\mathcal {O}})}$ consisting of a topological space X and a sheaf ${\displaystyle {\mathcal {O}}}$ of commutative ring spectra on X such that (1) the pair ${\displaystyle (X,\pi _{0}{\mathcal {O}})}$ is a scheme and (2) ${\displaystyle \pi _{k}{\mathcal {O}}}$ is a quasi-coherent ${\displaystyle \pi _{0}{\mathcal {O}}}$-module. The notion gives a homotopy-theoretic generalization of a scheme.

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