MATH 5020: Topics in Algebra

Local Field Theory (Spring 2019)

An introduction to the theory of local fields. We will introduce the p-adic numbers and their corresponding topology, build up the basic results in the subject, and use them to answer various problems in number theory. Some topics that I plan to address (given I have enough time): p-adic numbers, local-to-global principles, local Kronecker-Weber theorem, and higher ramification groups.

Spring 2019 syllabus