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Brave New Algebraic Geometry and global derived moduli spaces of ring spectra

Brave New Algebraic Geometry and global derived moduli spaces of ring spectra

. We develop homotopical algebraic geometry ([To-Ve 1, To-Ve 2]) in the special context where the base symmetric monoidal model category is that of spectra S, i.e. what might be called, after Waldhausen, brave new algebraic geometry. We discuss various model topologies on the model category of commutative algebras in …