2003/09/08 by Bertrand Toën, Bertrand Toen, Toen, Bertrand +2
Mathematics · Physics and Astronomy · #14A20 #18G55 #55P43 #55U40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AG #math.AT #msc:14A20 #msc:18G55 #msc:55P43 #msc:55U40
paper · pdf · doi:10.48550/arxiv.math/0309145
29 pages; some corrections and a new section
openalex publication_date 2003/09/08 · arxiv created 2004/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.