Math 254A: Number Theory
- 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.
Recommended literature: (not required)
- 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.
List of Topics:
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.
Final grades will be based on homework (including class participation), and a final project.