• Giorno - Ora: 25-11-2010 17:00
  • Luogo: Scuola Normale Superiore di PIsa (Aula Bianchi) - Relatore Clemens Fuchs, Politecnico ETH di Zurigo

Let K be a number field and let S be a finite set of places of K. A classical theorem of Shafarevich says that there are only finitely many K-isomorphism classes of elliptic curves over K with good reduction outside S. An effective version of this statement for K=Q was already proved by Coates. In the talk we discuss an extension to arbitrary number fields. We give explicit bounds and compare them with the one obtained by Coates. One of the important features of the result is that we view an elliptic curve as a purely geometric object which is natural and gives flexibility for further generalisations. This is joint work with R. von Känel and G. Wüstholz.