Time

Feb 23 2006 - 5:30pm

Location

CH 228

Speaker

Christian Schnell (The Ohio State University)

Abstract

A module over a ring $A$ is called flat if tensoring with that module leaves injective maps injective. A ring homomorphism $A \to B$ is said to be flat if $B$ is flat as an $A$-module. It turns out that flat ring homomorphisms have very many good algebraic properties, and these in turn make flatness a most useful notion in algebraic geometry as well. In this talk, I will try to explain the algebraic aspects of flatness. What is the meaning of the flatness condition? How can one tell whether a given ring homomorphism is flat? What makes flat ring homomorphisms better than non-flat ones? Go to the talk to learn the answers to these questions. This talk will only be about algebra, not about geometry. Later, however, there will likely be a second talk about the use of flatness in algebraic geometry.