M390C Algebraic Number Theory: Fall 2017

Day/Time: TTH 11am:-12:30pm; Location: RLM 12.166; Unique: 54615

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

Office Hours
Thursday 4-5pm 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. Contact me for more details if you are not sure whether this course is for you.

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

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.



This schedule is tentative and may be modified as necessary.

Date
Topics
  Aug. 31   Algebraic numbers and number fields
  Sept. 5, 7   Algebraic integers, Dedekind rings
  Sept. 12, 14   Factorization of ideals, Finiteness of the class group of rings of integers
  Sept. 19, 21   Lattices, Minkowski theory
  Sept. 26, 28   Discriminants, Primes in number fields
  Oct. 3, 5   Cyclotomic extensions
  Oct. 10, 12   Dirichlet's theorem
  Oct. 17, 19   Discriminants and Ramification
  Oct. 24, 26   Decomposition of prime ideals
  Oct. 31, Nov. 2   Local fields
  Nov. 7, 9   Continuation of local fields
  Nov 14, 16   Analytic methods
  Nov 21   Continuation of analytic methods
  Nov. 28, 30   Introduction to class field theory
  Dec. 5, 7   Class field theory