Recorded and posted by U Chicago grad student Zev Chonoles. What a strange and wonderful pleasure.
As we’ve seen, there is an analogy between Z and C[T]. In fact, the analogy between Z and Fp[T] is even stronger; for example the theory of zeta functions is very similar for Z and Fp[T]. We don’t know the true reason why they are so similar; perhaps they are children of the same parents. But we don’t know who their parents are; their parents are missing.
The class group is a bitter group and a sweet group. It is bitter because when it is non-trivial it
makes a mess. It is sweet because it makes things interesting.
There is a cake shop in Balmont, which is north of Chicago. The class group is the same as this
cake shop; it is a very nice cake shop.
I could go on but you should really just read these yourself.