Robert Garbary, Department of Pure Mathematics, University of Waterloo
“Separated and Proper Maps”
In the study of any kind of spaces, compact Hausdorff spaces play a very important role. Unfortunately, these concepts don’t really make sense for varieties (or schemes) because the Zariski topology is really stupid. The concepts are separatedness and properness are the appropriate analogy of Hausdorffness and compactness in the land of varieties (schemes). Of course, the concepts are relativized because that seems to be a popular thing to do. I’m going to talk about what these words mean.