Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture

ISBN-13: 9783540648635 / Angielski / Miękka / 1998 / 216 str.

Elisabeth Bouscaren

Opis

Illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang conjecture, this book updates developments in the applications of model theory to algebraic geometry. The detailed text includes comments and examples for the specialist and uninitiated.

Spis treści

to model theory.- to stability theory and Morley rank.- Omega-stable groups.- Model theory of algebraically closed fields.- to abelian varieties and the Mordell-Lang conjecture.- The model-theoretic content of Lang’s conjecture.- Zariski geometries.- Differentially closed fields.- Separably closed fields.- Proof of the Mordell-Lang conjecture for function fields.- Proof of Manin’s theorem by reduction to positive characteristic.