  For a (semi-)model category M, we define a notion of a ''homotopy''
Grothendieck topology on M, as well as its associated model category of stacks.
We use this to define a notion of geometric stack over a symmetric monoidal
base model category; geometric stacks are the fundamental objects to "do
algebraic geometry over model categories". We give two examples of applications
of this formalism. The first one is the interpretation of DG-schemes as
geometric stacks over the model category of complexes and the second one is a
definition of etale K-theory of E_{\infty}-ring spectra.
  This first version is very preliminary and might be considered as a detailed
research announcement. Some proofs, more details and more examples will be
added in a forthcoming version.
