18.786 - Algebraic Number Theory

Lecturer: Abhinav Kumar

Office: Room 2-169

Email: my_first_name [at] math . mit .edu

Lectures: TR 9:30 - 11 am, 2-131

Office Hours: W 5-6, F 3-4

Grader: Ruthi Hortsch

COURSE DESCRIPTION

An introduction to algebraic number theory. Dedekind domains, unique factorization of prime ideals. Number fields, splitting of primes, class group. Lattice methods, finiteness of the class number, Dirichlet's units theorem. Local fields, ramification, discriminants. Background in elementary number theory (e.g., 18.781) strongly recommended.

Prerequsites: 18.100 and 18.702

Text Book:

• Samuel, Algebraic Theory of Numbers
• Milne, Notes on algebraic number theory