Fall Quarter 2018, Math 225A, Algebraic Number Theory I


Instructor:
A. Agboola
Lecture:
TuTh 9:30am-10:45am, SH 1609

Office:
6724 South Hall
Office hours:
TuTh 11:00am--12:30pm (or by appointment)
Textbooks:
J. Neukirch, Algebraic Number Theory, Springer, (1999) (required).
P. Samuel, Algebraic Theory of Numbers, Dover, (2008) (required).
A. Frohlich, M. J. Taylor, Algebraic Number Theory, CUP, (1991) (recommended).


Homework:
The following link will take you to a problem sheet:

  • Problem sheet


    • Examinations:
    There will be no examinations given in this course.
    Course Outline:
    We shall aim to cover the following topics. Additional topics will be covered if time permits.

    Basic commutative algebra: Noetherian properties, integrality, rings of integers.

    More commutative algebra: Dedekind domains, unique factorisation of ideals, localisation.

    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 quadratic reciprocity.