Cornell Math - MATH 737, Fall 2006

MATH 737: Algebraic Number Theory (Fall 2006)

Instructor: Martin Kassabov

Meeting Time & Room

Prerequisites: Math 434 or equivalent.

Topics: This course is a basic introduction to algebraic number theory. The core of it deals with the ideal theory of Dedekind domains as applied to the rings of integers of number fields. A major purpose of the theory is to overcome the lack of unique factorisation into primes in these rings.

The course will also cover the fundamental finiteness theorems: the finiteness of the ideal class group, and the structure of the unit group. Additional topics which will be discussed if time permits: law of quadratic reciprocity, elementary Diophantine equations, completions (p-adic numbers), zeta-functions, distribution of primes in arithmetic progressions.