Geometry working seminar

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).