An Isaac Newton Institute Workshop

An Introduction to Recent Applications of Model Theory

Hilbert's Tenth Problem for function fields

6th April 2005

Author: Kirsten Eisentraeger (University of Michigan)

Abstract

We will discuss how elliptic curves of rank one can be used to prove undecidability of Hilbert's Tenth Problem for function fields of characteristic zero, such as R(t) and C(t_1,...,t_n) (n at least 2).

The approach for function fields of positive characteristic is very different, and we will sketch some of the methods used there.