  Profinite etale cobordism is a cohomology theory for smooth schemes of finite
type over a field. Using an idea of Friedlander, it is constructed as an etale
topological analog of the algebraic cobordism theories of Voevodsky and
Levine-Morel. With finite coefficients, profinite etale cobordism has a
converging Atiyah-Hirzebruch spectral sequence starting from etale cohomology.
There are interesting comparison maps from algebraic to profinite etale
cobordism. We conjecture that algebraic and etale cobordism with finite
coefficients are isomorphic after inverting a Bott element. For the development
of the theory, we construct a stable category of profinite spectra and an etale
realization of the category of stable motivic spectra over a field.
