Topics in Algebraic Number Theory

Illustration of Minkowski's theorem.

Some important properties of algebraic numbers follow from Minkowski's theorem: given a lattice in a Euclidean space, any bounded, convex, centrally symmetric region of large enough volume contains a nonzero lattice point. (Image courtesy of Jesus De Loera, Department of Mathematics, University of California, Davis. Used with permission.)

Instructor(s)

MIT Course Number

18.786

As Taught In

Spring 2006

Level

Graduate

Cite This Course

Course Features

Course Description

This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.

Kedlaya, Kiran. 18.786 Topics in Algebraic Number Theory, Spring 2006. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-786-topics-in-algebraic-number-theory-spring-2006 (Accessed). License: Creative Commons BY-NC-SA


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