Alan Thompson, Department of Pure Mathematics, University of Waterloo
“Yet more separatedness, and an introduction to projective schemes”
In this talk, I intend to begin by putting the final nail in the coffin of our prolonged discussion of separatedness. Of course, the next natural step would be an equally prolonged discussion of properness, but it’s the end of the term and we’re all tired, so something more concrete seems in order. For this reason, I will instead use the remainder of the talk to embark on a discussion of projective schemes, which are a bit more explicit and will greatly enlarge our collection of examples of non-affine schemes (and which, helpfully, will also provide some useful examples when we get around to talking about properness). I’ll start with a discussion of projective space and the Proj construction and, knowing how these things tend to go, probably not finish it.