Speaker: Bruce Olberding, New Mexico State University
Title: Local rings as points in topological spaces.
Abstract: The set of local subrings of a field can be endowed with a topology in a natural way. The features of this topology resemble, in a way that can be made precise, the features of the Zariski topology of the space of prime ideals of a ring. Some of these topological properties are reflected in the structure of the intersections of these rings, but other properties cannot be captured by topology alone. This way of viewing rings as points in a space underlies classical topics involving integral schemes, projective models, and the Zariski-Riemann space of valuation rings of a field. In this talk, we discuss applications, as well as limitations, of the topological point of view when dealing with intersections of rings.
