Winter Quarter 2006, Math 225A, Algebraic Number Theory I
TuTh 2:00pm-3:15pm, HSSB 1215
6724 South Hall, (805) 893-3844
D. A. Marcus, Number Fields, Springer, (1977) (required).
A. Frohlich, M. J. Taylor, Algebraic Number Theory, CUP,
The following link will take you to the homework assignments:
There will be no examinations given in this course.
We shall aim to cover the following topics. Additional topics will be
covered if time permits.
Basic commutative algebra: Noetherian properties, integrality, rings
More commutative algebra: Dedekind domains, unique factorisation of
Norms, traces and discriminants.
Decomposition of prime ideals in an extension field.
Class numbers and units. Finiteness of the class number: Minkowski
bounds. Dirichlet's unit theorem. Explicit calculation of units.
Decomposition of prime ideals revisited: the decomposition group and
the inertia group associated to a prime ideal. A nice proof of