Blake Madill, Pure Mathematics Department, University of Waterloo
“Introduction to the Structure Sheaf”
In this week’s seminar, we come one step closer to understanding schemes. It will turn out that a scheme is a topological space equipped with a sheaf, which is locally isomorphic to something we call an affine scheme. An affine scheme is something we will construct from a commutative ring R. This week, we present the ring theoretical background needed to un- derstand affine schemes. This includes an overview of Spec(R) and localization. We will then discuss the structure sheaf on Spec(R).