Nickolas Rollick, Department of Pure Mathematics, University of Waterloo
"Schemes at last"
All of our hard work is about to pay off - this week, we finally get to see the official definition of a scheme! But first, we will seek to understand the structure sheaf on an affine scheme through a couple examples, providing a satisfactory compliment to last week’s talk. Once the definition of a scheme is under our belts, we can complete another loose end we’ve left dangling - the correspondence between morphisms of affine schemes and morphisms of rings. Specifically, we will see that there is a bijection between scheme isomorphisms from Spec A to Spec B and ring isomorphisms from B to A. To conclude, we will get a feel for working with general schemes by discussing open subsets, disjoint unions, and stalks.
MC 5479