Title: ``Brave New'' Algebraic Geometry and global derived moduli spaces of ring spectra

Authors: Bertrand Toen, Gabriele Vezzosi 

Author's e-mail address: toen@picard.ups-tlse.fr ; vezzosi@dm.unibo.it

Other useful information: arXive submission 
numbermath.AT\0309145 

Abstract: We develop homotopical algebraic geometry (see math.AG/0207028)
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 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 as geometric S-stacks.