Spring 2010, Thursdays, Milner 216, 4:00-4:50 PM

Date: April 15

"  Localization "
  Piyush Shroff  


The idea of localization in a ring is extremely powerful and pervasive tool in algebra for isolating the behavior of the ideals in a ring. It is an algebraic analogue of the familiar idea of localizing at a point when considering questions of, for example, the differentiability of a function f(x) on the real line. In fact one of the important applications of this technique is to translate such "local" properties in the geometry of affine algebraic spaces to corresponding properties of their coordinate rings. In this talk I will give the definitions and simple properties of the formation of localization. Also I will do localization in modules.