Segal–Bargmann space
In algebraic geometry, a derived scheme is a pair consisting of a topological space X and a sheaf of commutative ring spectra [1] on X such that (1) the pair is a scheme and (2) is a quasi-coherent -module. The notion gives a homotopy-theoretic generalization of a scheme.
Just as affine algebraic geometry is equivalent (in categorical sense) to the theory of commutative rings (commonly called commutative algebra), affine derived algebraic geometry is (roughly in homotopical sense) equivalent to the theory of commutative differential graded rings.
Notes
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References
- P. Goerss, Topological Modular Forms [after Hopkins, Miller, and Lurie]
- B. Toën, Introduction to derived algebraic geometry
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- ↑ also often called -ring spectra