Sean O'Donnell, Temple University
This talk will introduce the long exact cohomology sequence and some basic theory surrounding it. We will begin by defining the cochain and cohomology functors, and then introduce the long exact sequence and discuss its naturality. The structure of this exact sequence will motivate us to investigate acyclic, cohomologically trivial, and induced modules, which we will then use to introduce the technique of dimension shifting. During this, we will also discuss the application of these structures to the cohomology of Galois groups acting on the additive groups of their relevant fields.