Algebraic Geometry Learning Seminar

Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo

"Topological properties of $Spec(A)$"

We will describe properties of points of affine schemes. First, we will introduce the concepts of  "closed points", "specialization" and "generalization" and see some examples. Next, we will describe the noetherian condition for a topological space and show that every closed set in a noetherian space can be splitted in a finite number of pieces. Finally, we introduce the function $I(\cdot)$ and show that $I(\cdot)$ and $V(\cdot)$ give a bijection between subsets of $Spec(A)$ and radical ideals of $A$.

MC 5479