**Note: To curb Covid-19 spread, from 18 Mar., 2020 on, we have switched to online lecture delivery via Zoom meeting. The URL and instruction for accessing the Zoom meeting are available on Canvas.**

**Day/Time:**M 15:15 - 16:15, W 09:00 - 10:00, F 12:00 - 13:00 (2 Mar. - 5 June, 2020)**
Location:** Peter Hall G03 (Evan Williams Theatre) Zoom Meeting

**Chenyan Wu**

Instructor:

Instructor:

**Contact Information:**chenyan.wu "at" unimelb.edu.au

**Office Hour:**Zoom Meeting at M 16:15 - 17:15, W 11:00 - 12:00, Th 16:20 - 17:20 and by email.

**Office:**Peter Hall Building 208 (¯\_(ツ)_/¯)

**Textbook:**Algebraic Theory of Numbers by Pierre Samuel

### Prerequisites:

The students should be familiar with concepts of vector spaces, groups and rings.

### Course Description:

This course is an introduction to algebraic number theory. Algebraic number theory studies the structure of the integers and algebraic numbers, combining methods from commutative algebra, complex analysis, and Galois theory. This subject covers the basic theory of number fields, rings of integers and Dedekind domains, zeta functions, decomposition of primes in number fields and ramification, the ideal class group, and local fields. Additional topics may include Dirichlet L-functions and Dirichlet’s theorem; quadratic forms and the theorem of Hasse-Minkowski; local and global class field theory; adeles; and other topics of interest.

### Assessment:

Grade is based on assignments (50%: 3 assignments (up to 50 pages) worth 15%, 15%, 20% respectively, spread evenly throughout the semester). A take-home open-book written examination (50%, during the exam period).

### Recommended Books:

These books, of course, go much beyond the scope of our subject material.

The following three give very accessible and modern account of the subject.

- Number Theory 1 - Fermat's Dream by Kazuya Kato, Nobushige Kurokawa and Takeshi Saito;
- Number Theory 2 - Introduction to Class Field Theory by Kazuya Kato, Nobushige Kurokawa and Takeshi Saito;
- Number Theory 3 - Iwasawa Theory and Modular Forms by Nobushige Kurokawa, Masato Kurihara and Takeshi Saito;

It looks there is no need to mention the title of the books at all. They are all very good. You need to see which one speaks to you.

- Algebraic Number Theory edited by Cassels and Fröhlich
- Algebraic Number Theory by James Milne, downloadable at https://www.jmilne.org/math/CourseNotes/
- Algebraic Number Theory by Serge Lang
- Algebraic Number Theory by Jürgen Neukirch