I realize I’ve been falling a bit behing in the typed up lecture notes, but I do want to emphasise that there are things which are in the notes which have not been done in as much detail in the course lectures. Hopefully I’ll have a chance to put in the proof of the compatibility between the Brauer group operation and the multiplication of 2-cocycles in the near future.

Today, we’ll be moving forward with Galois cohomology in some more detail, describing in particular the long exact sequences and boundary maps, and using these to obtain information on the period and index. Assuming we get through this, we’ll continue on to start discussing involutions!

Much of the material I have been using to date comes from Pierce’s Associative algebras book. Today I’ll also be drawing from Serre’s Galois Cohomology, as well as the Book of Involutions.