Algebraic Number Theory
(March14-25,2005)
SMS is organizing a short course on algebraic number theory. The course lectures will be given by Mark Bashmakov (IPLE, Berlin). All interested are invited to register, preferably before March 12, 2005. Registration is free and participation is by invitation only. To register please send a copy of the CV to choudary@cwu.edu. For further information, contact: choudary@cwu.edu
The course will give an overview of the modern
algebraic number theory.
It is based on the classical monographs of Hecke, H. Weil,
Borevitch-Shafarevitch,
A. Weil, Serre, Tate. Text books available in the SMS
library will be used during
the course.
Outline of the course
1) Metrics of the rational fields. Completions.
P-adic numbers.
Principle of Minkovsky-Hasse. Quadratic Forms.
2) Algebraic extensions of the rational field.
Quadratic and cyclotomic fields.
Factorization of prmes. Units. Theorem of Dirichlet.
3) Rings of integers in algebraic number fields.
Group of classes. Its finiteness.
Analytic formulae for the class number.
4) Theory of ramifications. Unramified extensions.
Local fields. Structure if the
multiplicative group. Ramifications in the local fields.
5) Simple central algebras. Hasse symbols. Reciprocity
laws. Introduction to the
class field theory.