Algebraic number theory notes
Note: These notes are based on talks given in a study group I organised amongst the Bristol postgraduate number theorists between 2008 and 2010. They are assuredly full of errors and misunderstandings, since that's how we learn. In short: if you plan to read these notes to learn something about algebraic number theory then you're going to have a bad time. Try James Milne's notes here instead.
2008-2009
- Lecture 1: A brief history
- Lecture 2: Algebraic numbers, an introduction
- Lecture 3: Conjugates et al.
- Lecture 4: Quadratic and cyclotomic fields, and more besides
- Lecture 5: Ideals in rings of integers
- Lecture 6: From unique factorisation to class groups
- Lecture 7: A recap via the medium of examples
- Lecture 8: Finiteness of the class number
- Lecture 9: Hilbert's ramification theory
- Lecture 10: Über das Gaußsche Reziprozitätsgesetz
- Lecture 11: L-series and theta series
- Lecture 12: The Dedekind zeta function
- Lecture 13: Dirichlet and his unit theorem
- Lecture 14: Kummer theory
- Lecture 15: A brief introduction to profinite groups
2009–2010
- Lecture 16: Fifteen to one
- Lecture 17: Galois cohomology
- Lecture 18: Valuations
- Lecture 19: The Hilbert Symbol
- Lecture 22: Unramification
- Lecture 23: The main results of class field theory, based on these notes
