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

Bertrand Toen·Gabriele Vezzosi
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Abstract

We develop homotopical algebraic geometry (see math.AG/0207028) in the special context where the base symmetric monoidal model category is the category S of spectra, 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 S, the associated theories of geometric S-stacks (a geometric S-stack being an analog of Artin notion of algebraic stack in Algebraic Geometry), and finally show how to define global moduli spaces of associative ring spectra structures and a moduli space related to topological modular forms as geometric S-stacks.

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Bertrand Toen, Gabriele Vezzosi. 2004-06-29. "Brave New" Algebraic Geometry and global derived moduli spaces of ring spectra. https://arxiv.org/abs/math/0309145

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