"Brave New" Algebraic Geometry and global derived moduli spaces of ring spectra
Algebraic Topology
2007-05-23 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0309145,
title = {"Brave New" Algebraic Geometry and global derived moduli spaces of ring spectra},
author = {Bertrand Toen and Gabriele Vezzosi},
journal= {arXiv preprint arXiv:math/0309145},
year = {2007}
}
Comments
29 pages; some corrections and a new section