Franz Lemmermeyer

Class Field Theory

Seminar: Class Field Theory a la Hasse. English translation of Hasse's `Vorlesungen über Klassenkörpertheorie. My intention is to cover Part I: Galois Theory in this semester.
What should you expect? First of all a very explicit introduction to Galois theory (the Lectures are from 1932, today's standard version of Galois theory was created in Artin's Notre Dame lectures in the 1950s). Actually Hasse deals only with fields of characteristic 0, thus avoiding the problems with inseparable extensions. He then discusses applications of Galois theory to algebraic number theory (Hilbert's theory of ramification, connections with the local theory of finite extensions of the p-adic numbers), and finally introduces the Artin symbol.
Prerequisites: abstract algebra (homomorphisms, factor groups).


We will meet Wednesday 3:40 except on days when there's a general seminar.


Here's the first chapter covering Galois theory proper, Hilbert's ramification groups, and the Artin symbol. If you observe any typos or strange formulations, please let me know. Here are a few problems we may discuss.