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In algebraic geometry, a derived scheme is a pair {\displaystyle } consisting of a topological space X and a sheaf O {\displaystyle {\mathcal {O}}} either of simplicial commutative rings or of commutative ring spectra on X such that the pair {\displaystyle } is a scheme and π k O {\displaystyle \pi _{k}{\mathcal {O}}} is a quasi-coherent π 0 O {\displaystyle \pi _{0}{\mathcal {O}}} -module. The notion gives a homotopy-theoretic generalization of a scheme.
A derived stack is a stacky generalization of a derived scheme.
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