Class Field Theory

Time: the fourth semester

Credit: 3 hours

Period: 54 hours

Previous courses: Abstract Algebra, Algebraic number theory

Syllabus:

(1) Norm Index Computation

(2) Local Class Field Theory

(3) Global Class Field Theory

(4) The Kronecker-Weber Theorem

(5) Artin L-Functions

(6) Weil Groups and Artin-Hecke L-Functions

References:

(1) J. W. S. Cassels and A. Frohlich, Algebraic Number Theory, Thompson Publishing Co., 1967.

(2) S. Lang, Algebraic Number Theory, Springer-Verlag, GTM 110.

(3) J. S. Milne, Class Field Theory, available at http://www.jmilne.org/math/.

(4) J. Tate, Number Theoretic Background, PSPM, Vol. 33, AMS, 1979, Part 2, 3-26.