M390C Algebraic Number Theory: Spring 2012

Day/Time: TTH 11am-12:30m; Location: RLM 9.166; Unique: 56120

Instructor
Mirela Ciperiani (mirela at math dot utexas dot edu); Office: RLM 12.164

Office Hours
Wednesday 5pm-6pm in RLM 12.164.

References:
Z. I. Borevich and I. R. Shafarevich, Number Theory
J.W.S. Cassels and A. Frohlich, Algebraic Number Theory
A. Frohlich and M.J.Taylor, Algebraic Number Theory
S. Lang, Algebraic Number Theory
J.S Milne, Algebraic Number Theory
J. Neukirch, Algebraic Number Theory

We will cover most of the material of the first two chapters of the book by Neukirch.

Prerequisites
M380C&D. If you are not sure if this course is for you contact me for more details.

Grading
Plus/minus grades will be assigned for the final grade in this course.
There will be weekly homework assignments.

Disabilities
Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities, 512-471-6259. If you plan on using accommodations, you need to notify the instructor by the 12-th class day.



The topics will be posted as the course progresses.

Date
Topics
  Jan. 17, 19   Algebraic numbers and number fields, Algebraic integers
  Jan. 24, 26   Dedekind rings, Factorization of ideals
  Jan. 31, Feb. 2   Finiteness of the class group of rings of integers
  Feb. 7, 9   Lattices, Minkowski theory
  Feb.14, 16   Discriminants, Primes in number fields
  Feb. 21, 23   Cyclotomic extensions
  Feb. 28, Mar. 1   Dirichlet's theorem
  Mar. 6, 8   Discriminants and Ramification
  Mar. 20, 22   Decomposition of prime ideals
  Mar. 27, 29   Local fields
  Apr. 3, 5   Continuation of local fields
  Apr. 10, 12   Analytic methods
  Apr. 17, 19   Continuation of analytic methods
  Apr. 24, 26   Introduction to class field theory
  May 1, 3   Continuation of introduction to class field theory