  We show that the existence of rational points on smooth varieties over a
field can be detected using homotopy fixed points of etale topological types
under the Galois action. As our main example we show that the surjectivity
statement in Grothendieck's Section Conjecture would follow from the
surjectivity of the map from fixed points to continuous homotopy fixed points
on the level of connected components. Along the way we define a new model for
the continuous etale homotopy fixed point space of a smooth variety over a
field under the Galois action.
