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
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.