Model Theory and Algebraic Geometry / Lecture Notes in Mathematics Bd.1696 (PDF)

This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject. TOC:Introduction to model theory.- Introduction to stabilitiy theory and Morley rank.- Omega-stable groups; Model theory of algebraically closed fields.- Introduction to abelian varieties and the Mordell-Lang conjecture.- The model-theoretic content of Lang's conjecture.- Zariski geometries.- Differential closed fields.- Separably closed fields.- Proof of the Mordell-Lang conjecture for function fields.- Proof of Manin's theorem by reduction to positive characteristic.- Index.