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

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

2003-09-08

arxiv.org/abs/math/0309145v2

Mathematics

Algebraic Topology

29 pages; some corrections and a new section

Scientific paper

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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