Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine prob

An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory.

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite att

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Represent

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic g