Global Class Field Theory and Complex Multiplication

   Seminar :

  The Seminar will be run by Aprameyo Pal and Carlos de Vera Piquero.

  Please ask us in case of any question.

  aprameyo.pal@uni-due.de or 

  carlos.de-vera-piquero@uni-due.de

   Contents :

  Starting with a classical problem from elementary number theory about the representation of prime numbers by binary quadratic forms, in this seminar we will give an introduction to both global class field theory and complex multiplication from a classical point of view. The ultimate  goal will be to relate these two remarkably rich areas in number theory through the theory of modular elliptic functions.

  Depending on the background and interests of the participants, we will adapt the contents of the seminar and the distribution of the topics.

  Prerequisites:

  Students are expected to be familiar with Galois Theory and to have a basic knowledge of Algebraic Number Theory.

  References:

 1) Primes of the Form x^2 + ny^2 by David Cox

 2) Algebraic Number Theory by S. Lang