We will cover pieces of I-VII of "Algebraic
Number Theory" by Cassels-Froehlich. The focus will be on the local theory, and time permitting we will talk about Global CFT and compatibility.
There will be no exams or collected homework, but I will post homework
every week which you should absolutely make a serious attempt to complete (or at least think
about for a while) since the subject is a difficult one to learn and hence active engagement with
the concepts in both theoretical and concrete settings is imperative for success. There will also be
some handouts to supplement the lectures.
Homework will be posted as a single pdf here. The tex file for this is here, and you will find hints in the comments.
All of the material in this course is fundamental background material for everyone taking the course. The expectation is that you will set aside time between each pair of lectures to review the material, and will collaborate with classmates and approach me with questions about, literally, anything that you don't understand.
Topics from class
Point set topology: ch 1-2 of Munkres or Armstrong.
Profinite groups: [CF, V]
Infinite Galois Theory: [CF, V.1.6]
If you've never seen Qp before, I recommend checking out Gouvea's "p-adic numbers An intro"
The more standard references are Neurkirch's "Algebraic Number Theory", Ch II, and Lang's "Algebraic Number Theory"