Math 80220 Topics in Algebra 2 (Spring
2014)
Introduction to Algebraic Number Theory
- Topics:
- Number fields and number rings
- Class groups and class numbers
- Unique factorization into primes ideals
- Minkowski's geometry of numbers
- Kummer's special cases of Fermat's Last Theorem
- Quadratic forms
- Galois theory and ramification
- The Dirichlet unit theorem
- Zeta functions and the class number formula
- L-functions and primes in arithmetic progressions
- Special values of zeta functions
