Nickolas Rollick, Department of Pure Mathematics, University of Waterloo
"A quasi-separated talk"
This week's talk will blur the lines between last week's discussion of projective schemes and our upcoming goal of discussing properties of schemes. So blurred, in fact, that the two are only quasi-separated! We start by formally defining projective and quasiprojective schemes over a ring, and we look at "closed subsets of projective space over a field". This segues nicely into a discussion of topological properties of schemes in general, when we prove that projective space over a field is irreducible. What follows is a gallery of observations about various types of schemes, with the apex being the introduction of quasi-separated schemes. We will characterize the so-called qcqs (quasi-compact and quasi-separated) schemes, and we will notice in particular that projective schemes over a ring are qcqs.
MC 5479