**Faculty:**Adam Topaz.**Lecture:**MWF 11-12P, in 31 Evans.**Office Hours:**MF 12:10-1:10pm.**Office Number:**889 Evans.**Syllabus:**pdf will be available here soon.

*Algebraic Number Theory,*by**S. Lang.***Algebraic Number Theory,*by**J. Neukirch.***Algebraic Number Theory,*by**J.S. Milne**(notes freely available online).*Algebraic Number Theory,*edited by**J.W.S. Cassels**and**A. Fröhlich.**- … other sources will be discussed in class.

A strong background in graduate-level algebra, including Galois theory, tensor products, polynomial rings, localization, etc., is required for this course. Here is a (somewhat ambitious) list of the topics I hope to cover in this class, time permitting. This list is *tentative* and will likely change with the interests of the participants.

- Integral closure, localization, and other required basics from commutative algebra.
- Dedekind rings, global fields, rings of integers, factorization of ideals, curves over finite fields, Spec of a commutative ring.
- Geometry of numbers, class groups, unit groups.
- Cyclotomic extensions and quadratic extensions.
- Valuations, ramification and decomposition theory.
- Completions, local fields, ideles and adeles.
- Selected topics from (local) class field theory and basics of Galois cohomology.
- A bit on zeta functions and
*L*-functions, distribution of primes.

- Homework 1
- Homework 2
- Homework 3
- Homework 4
- Homework 5 (placeholder)
- Homework 6 (placeholder)

Final grades will be based on homework (including class participation), and a final project.