Topology Seminar: R.Jardine

We start with a general introduction to pro-objects in topological and geometric settings, with descriptions of well-known examples, including Postnikov towers, absolute Galois groups, and etale homotopy types. This is followed by a brief discussion of homotopy theories of pro-objects. Homotopy theoretic techniques are applied to give the first correct comparison of finite descent and Galois cohomological descent for simplicial presheaves on the etale site of a field. Examples arise in the study of algebraic K-theory with finite coefficients over a field.