Title: Higher ramification groups and counting Galois extensions
Abstract: This is a follow-up to last week's talk on nilpotent Artin-Schreier theory. We recall some basic facts about higher ramification groups of Galois extensions and where they come up in class field theory. Then, we study how they fit in with Abrashkin's nilpotent Artin-Schreier theory, and we sketch how we can (for some groups G) count G-extensions by an invariant arising from the last jumps in the ramification filtration.