Math 201A: Basic Topics in Algebra (Fall 2010)

This is the web site for Math 201A (Basic Topics in Algebra) for the fall 2010 quarter. The specific topic for this course is "Arithmetic of Local Fields". The plan is to give a rigorous introduction to the theory of local fields (such as the p-adic numbers), including ramification theory, some local class field theory, and perhaps a bit of p-adic Hodge theory. We'll follow Serre's book (see below) to the extent that the material I have in mind appears therein.

Some basic facts:

Instructor: Kiran Kedlaya (kedlaya[at]ucsd[dot]edu), APM 7402 (office hours: Wednesdays 4-5 or by appointment)
Lectures: MWF 3-4, APM 5829. No lectures during the week of Thanksgiving (November 22-26).
Textbook: Serre, Local Fields, Springer-Verlag. I will supplement with typed lecture notes, posted as one cumulative file. (Please report typos!)
Prerequisites: Algebraic number theory, ideally (no pun intended) with some mention of p-adic numbers. Some basic commutative algebra might be helpful too.
Homework: None unless you need a grade (see below). I will mark some exercises in the notes, though, in case you want to test your understanding (which is strongly encouraged).
Exams: None. Ignore what Blink says about the final exam; there is none.
Grading: None unless you need a meaningful grade (e.g., if you are an undergraduate). In that case, check with me to find out how much homework you should plan to turn in.