Submission date: 10 December 2014.

Abstract:

Preprint, to appear in the forthcoming LMS Lecture Note series, O-Minimality and Diophantine Geometry, published by Cambridge Univeristy Press. Originating from a short LMS-EPSRC course held at the Univerisity of Manchester.

The purpose of this article is to explain the Pila-Zannier strategy for proving the André-Oort conjecture. First, however, we will provide a brief introduction to the theory of Shimura varieties.

Mathematics Subject Classification: 11G18, 14G35, 03C64

Keywords and phrases:

Full text arXiv 1412.3237: pdf, ps.