The paper is a survey of geometric model theory based on the tutorial given by the author at Logic Colloquium 2000 in Paris. The main goal was to tell logicians from other parts of logic about recent applications of model theory to diophantine geometry, discovered by E. Hrushovski. First, the author discusses the theory of algebraically closed fields, which is the model-theoretic context for classical algebraic geometry, and explains how the Mordell-Lang and Manin-Mumford conjectures fit within the model-theoretic framework. Then she defines and discusses independence and local modularity, and illustrates the notions by basic examples. She presents the theories of differentially closed fields of characteristic zero and algebraically closed fields with an automorphism, which are used in Hrushovski’s model-theoretic proof of the Manin-Mumford conjecture. Then a brief sketch of the strategy for the proof is given. The paper contains a list of references for further reading.
For the entire collection see [Zbl 1064.03003].