SURVEY OF DIOPHANTINE GEOMETRY

Contents:

Some qualitative Diophantine statements

Heights and rational points

Abelian varieties

Faltings’ finiteness theorems on Abelian varieties and curves

Modular curves over Q

The geometric case of Mordell’s conjecture

Arakelov theory

Diophantine problems and Complex geometry

Well functions, integral points and Diophantine approximations

Existence of many rational points