**Title of the course:** Imaginary quadratic fields and elliptic curves with complex multiplication

**Instructor:** Dr. Pınar Kılıçer

**Institution:** Carl von Ossietzky Universitat Oldenburg

**Dates:** 7-13 August 2017

**Prerequisites:** Group theory, ring theory, and field theory.

**Level:** Graduate, advanced undergraduate

**Abstract:** We will start with number fields; orders in number fields, ramification of primes, the ideal class number etc.

Then we will focus on quadratic fields, especially imaginary quadratic fields. We will study the basics of class field theory

and especially the Hilbert class field of imaginary quadratic fields. Then finally, we will show a relationship between

elliptic curves (elliptic curves will be studied at the same week by Dino Festi) and the Hilbert class field of imaginary quadratic fields.

**Textbook or/and course webpage:** David Cox, Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication.

**Language: **EN